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<!DOCTYPE html><html><head><title>A Course on Group Theory - John S. Rose - Google Books</title><link rel="stylesheet" href="/books/css/_a33f2a89320471e58c940b9287b9d4eb/kl_about_this_book_kennedy_full_bundle.css" type="text/css" /><link rel="stylesheet"href="https://fonts.googleapis.com/css2?family=Product+Sans:wght@400"><link rel="canonical" href="https://books.google.com/books/about/A_Course_on_Group_Theory.html?id=j-I7Zpq3GdIC"/><meta property="og:url" content="https://books.google.com/books/about/A_Course_on_Group_Theory.html?id=j-I7Zpq3GdIC"/><meta name="title" content="A Course on Group Theory"/><meta name="description" content="This textbook for advanced courses in group theory focuses on finite groups, with emphasis on the idea of group actions. Early chapters summarize presupposed facts, identify important themes, and establish the notation used throughout the book. Subsequent chapters explore the normal and arithmetical structures of groups as well as applications. Topics include the normal structure of groups: subgroups; homomorphisms and quotients; series; direct products and the structure of finitely generated Abelian groups; and group action on groups. Additional subjects range from the arithmetical structure of groups to classical notions of transfer and splitting by means of group action arguments. More than 675 exercises, many accompanied by hints, illustrate and extend the material."/><meta property="og:title" content="A Course on Group Theory"/><meta property="og:type" content="book"/><meta property="og:site_name" content="Google Books"/><meta property="og:image" content="https://books.google.com.sg/books/content?id=j-I7Zpq3GdIC&printsec=frontcover&img=1&zoom=1&edge=curl&imgtk=AFLRE70gFe2HatUYUa1z_bCOdKPbewRqmUWBj2Q2rgEmvzfdgYLuYYvDbXj7vd16qM4IQJJndrNGNbrqqR0qULOp-ZrANFjXAFocTD9oxJXUlQ80WtK_4qkdIMTpa8gVooYu1pI0PTp5"/><link rel="image_src" href="https://books.google.com.sg/books/content?id=j-I7Zpq3GdIC&printsec=frontcover&img=1&zoom=1&edge=curl&imgtk=AFLRE70gFe2HatUYUa1z_bCOdKPbewRqmUWBj2Q2rgEmvzfdgYLuYYvDbXj7vd16qM4IQJJndrNGNbrqqR0qULOp-ZrANFjXAFocTD9oxJXUlQ80WtK_4qkdIMTpa8gVooYu1pI0PTp5"/><script></script><style>#gbar,#guser{font-size:13px;padding-top:1px !important;}#gbar{height:22px}#guser{padding-bottom:7px !important;text-align:right}.gbh,.gbd{border-top:1px solid #c9d7f1;font-size:1px}.gbh{height:0;position:absolute;top:24px;width:100%}@media all{.gb1{height:22px;margin-right:.5em;vertical-align:top}#gbar{float:left}}a.gb1,a.gb4{text-decoration:underline !important}a.gb1,a.gb4{color:#00c !important}.gbi .gb4{color:#dd8e27 !important}.gbf .gb4{color:#900 !important} #gbar { padding:.3em .6em !important;}</style></head><body class=""><div id=gbar><nobr><a target=_blank class=gb1 href="https://www.google.com.sg/search?tab=pw">Search</a> <a target=_blank class=gb1 href="https://www.google.com.sg/imghp?hl=en&tab=pi">Images</a> <a target=_blank class=gb1 href="https://maps.google.com.sg/maps?hl=en&tab=pl">Maps</a> <a target=_blank class=gb1 href="https://play.google.com/?hl=en&tab=p8">Play</a> <a target=_blank class=gb1 href="https://www.youtube.com/?tab=p1">YouTube</a> <a target=_blank class=gb1 href="https://news.google.com/?tab=pn">News</a> <a target=_blank class=gb1 href="https://mail.google.com/mail/?tab=pm">Gmail</a> <a target=_blank class=gb1 href="https://drive.google.com/?tab=po">Drive</a> <a target=_blank class=gb1 style="text-decoration:none" href="https://www.google.com.sg/intl/en/about/products?tab=ph"><u>More</u> »</a></nobr></div><div id=guser width=100%><nobr><span id=gbn class=gbi></span><span id=gbf class=gbf></span><span id=gbe></span><a target=_top id=gb_70 href="https://www.google.com/accounts/Login?service=print&continue=https://books.google.com.sg/books%3Fid%3Dj-I7Zpq3GdIC%26redir_esc%3Dy%26hl%3Den%26output%3Dhtml_text&hl=en&ec=GAZACg" class=gb4>Sign in</a></nobr></div><div class=gbh style=left:0></div><div class=gbh style=right:0></div><div class="kd-appbar"><h2 class="kd-appname"><a href="/books">Books</a></h2><div class="kd-buttonbar left" id="left-toolbar-buttons"><a id="appbar-view-print-sample-link" href="https://books.google.com.sg/books?id=j-I7Zpq3GdIC&printsec=frontcover&output=html_text&source=gbs_atb"></a><a id="appbar-view-ebook-sample-link" href=""></a><a id="appbar-patents-prior-art-finder-link" href=""></a><a id="appbar-patents-discuss-this-link" href="" data-is-grant=""></a><a id="appbar-read-patent-link" href=""></a><a id="appbar-download-pdf-link" href=""></a></div><div class="kd-buttonbar right" id="right-toolbar-buttons"></div><script>(function() {var div = document.getElementById('left-toolbar-buttons');var links = div.getElementsByTagName("a");for (var i = links.length - 1; 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Rose</span></a></div><div><span dir=ltr>Courier Corporation</span>, <span dir=ltr>1 Jan 1994</span> - <a class="secondary" href="https://www.google.com.sg/search?tbo=p&tbm=bks&q=subject:%22Mathematics%22&source=gbs_ge_summary_r&cad=0"><span dir=ltr>Mathematics</span></a> - <span dir=ltr>310 pages</span></div></div><div id=synopsis><div id=synopsis-window><div id=synopsistext dir=ltr class="sa">This textbook for advanced courses in group theory focuses on finite groups, with emphasis on the idea of group actions. Early chapters summarize presupposed facts, identify important themes, and establish the notation used throughout the book. Subsequent chapters explore the normal and arithmetical structures of groups as well as applications.<br> Topics include the normal structure of groups: subgroups; homomorphisms and quotients; series; direct products and the structure of finitely generated Abelian groups; and group action on groups. Additional subjects range from the arithmetical structure of groups to classical notions of transfer and splitting by means of group action arguments. More than 675 exercises, many accompanied by hints, illustrate and extend the material.</div></div></div><div class="search_box_wrapper"><div id="preview-link"><a href="https://books.google.com.sg/books?id=j-I7Zpq3GdIC&printsec=frontcover&output=html_text" class="primary"><span dir=ltr>Preview this book</span> »</a></div></div></td> </tr></table><div id="summary-second-column"></div></div></div></div></div><div class=vertical_module_list_row><h3 class=about_title><a name="search_anchor"></a>From inside the book</h3><div id=search class=about_content><form action=/books?source=gbs_search_r&cad=1 id=search_form method=get> <input type=hidden name="redir_esc" value="y"><input type=hidden name="output" value="html_text"><input type=hidden name="id" value="j-I7Zpq3GdIC"><input type="hidden" name="focus" value="searchwithinvolume"><input id=search_form_input type=text maxlength=1024 name=q value="" title="Search" accesskey="i" aria-label="Search in this book" style="width:160px"><script type="text/javascript">if (window['_OC_autoDir']) {_OC_autoDir('search_form_input');}</script> <input type=submit value="Search"></form><div id=search_v><div id="searchwithinvolume" tabindex="0"></div></div></div></div><div class=vertical_module_list_row><h3 class=about_title><a name="selected_pages_anchor"></a>Selected pages</h3><div id=selected_pages class=about_content><div id=selected_pages_v><div class="selectedpagesthumbnail"><a href="https://books.google.com.sg/books?id=j-I7Zpq3GdIC&pg=PR3&output=html_text&source=gbs_selected_pages&cad=2" ><img src="https://books.google.com.sg/books/content?id=j-I7Zpq3GdIC&pg=PR3&img=1&zoom=1&sig=ACfU3U0gk7P_kMkimKtG3sik01LqrD0YbA" alt="Title Page" title="Title Page" height="160" border="1"></a><br/><a class="primary" href="https://books.google.com.sg/books?id=j-I7Zpq3GdIC&pg=PR3&output=html_text&source=gbs_selected_pages&cad=2" >Title Page</a></div><div class="selectedpagesthumbnail"><a href="https://books.google.com.sg/books?id=j-I7Zpq3GdIC&pg=PR5&output=html_text&source=gbs_selected_pages&cad=2" ><img src="https://books.google.com.sg/books/content?id=j-I7Zpq3GdIC&pg=PR5&img=1&zoom=1&sig=ACfU3U04QAMOw_ijN47MeCUxoOHHcQlxJA" alt="Table of Contents" title="Table of Contents" height="160" border="1"></a><br/><a class="primary" href="https://books.google.com.sg/books?id=j-I7Zpq3GdIC&pg=PR5&output=html_text&source=gbs_selected_pages&cad=2" >Table of Contents</a></div><div class="selectedpagesthumbnail"><a href="https://books.google.com.sg/books?id=j-I7Zpq3GdIC&pg=PA301&output=html_text&source=gbs_selected_pages&cad=2" ><img src="https://books.google.com.sg/books/content?id=j-I7Zpq3GdIC&pg=PA301&img=1&zoom=1&sig=ACfU3U2NFfAiS0iPDBguoIYSyynmPMJ5NQ" alt="Index" title="Index" height="160" border="1"></a><br/><a class="primary" href="https://books.google.com.sg/books?id=j-I7Zpq3GdIC&pg=PA301&output=html_text&source=gbs_selected_pages&cad=2" >Index</a></div><div class="selectedpagesthumbnail"><a href="https://books.google.com.sg/books?id=j-I7Zpq3GdIC&pg=PA298&output=html_text&source=gbs_selected_pages&cad=2" ><img src="https://books.google.com.sg/books/content?id=j-I7Zpq3GdIC&pg=PA298&img=1&zoom=1&sig=ACfU3U1aIk_zg1txIMB80nVd-nc5O6MAAg" alt="References" title="References" height="160" border="1"></a><br/><a class="primary" href="https://books.google.com.sg/books?id=j-I7Zpq3GdIC&pg=PA298&output=html_text&source=gbs_selected_pages&cad=2" >References</a></div><div style="clear:both;"></div></div></div></div><div class=vertical_module_list_row><h3 class=about_title><a name="book_other_versions_anchor"></a>Other editions - <a href='https://books.google.com.sg/books?q=editions:ISBN0486681947&id=j-I7Zpq3GdIC&output=html_text'>View all</a></h3><div id=book_other_versions class=about_content><div id=book_other_versions_v><div class="one-third-column"><div class="crsiwrapper"><table class="rsi" cellspacing=0 cellpadding=0 border=0><tr><td class="coverdstd" align="center"><a href="https://books.google.com.sg/books?id=TWDCAgAAQBAJ&output=html_text&source=gbs_book_other_versions_r&cad=3" ><img alt="" class="coverthumb hover-card-attach-point" src="https://books.google.com.sg/books/content?id=TWDCAgAAQBAJ&printsec=frontcover&img=1&zoom=5&edge=curl" border="0" height="80"></a></td><td valign=top><div class=resbdy><a class="primary cresbdy" href="https://books.google.com.sg/books?id=TWDCAgAAQBAJ&printsec=frontcover&output=html_text&source=gbs_book_other_versions_r&cad=3"><span dir=ltr>A Course on Group Theory</span></a><br><span style="line-height: 1.3em; font-size:-1;"><span><a href="https://www.google.com.sg/search?tbo=p&tbm=bks&q=inauthor:%22John+S.+Rose%22" class="secondary"><span dir=ltr>John S. Rose</span></a></span><br/><span><span style="color:#99522e">Limited preview</span> - 2013</span><br/></span></div></td><td align=right></td></tr></table></div></div><div class="one-third-column"><div class="crsiwrapper"><table class="rsi" cellspacing=0 cellpadding=0 border=0><tr><td class="coverdstd" align="center"><a href="https://books.google.com.sg/books?id=pYk6AAAAIAAJ&output=html_text&source=gbs_book_other_versions_r&cad=3" ><img alt="" class="coverthumb hover-card-attach-point" src="https://books.google.com.sg/books/content?id=pYk6AAAAIAAJ&printsec=frontcover&img=1&zoom=5&edge=curl" border="0" height="80"></a></td><td valign=top><div class=resbdy><a class="primary cresbdy" href="https://books.google.com.sg/books?id=pYk6AAAAIAAJ&printsec=frontcover&output=html_text&source=gbs_book_other_versions_r&cad=3"><span dir=ltr>A Course on Group Theory</span></a><br><span style="line-height: 1.3em; font-size:-1;"><span><a href="https://www.google.com.sg/search?tbo=p&tbm=bks&q=inauthor:%22John+S.+Rose%22" class="secondary"><span dir=ltr>John S. Rose</span></a></span><br/><span><span style="color:#99522e">Limited preview</span> - 1978</span><br/></span></div></td><td align=right></td></tr></table></div></div><div class="one-third-column"><div class="crsiwrapper"><table class="rsi" cellspacing=0 cellpadding=0 border=0><tr><td class="coverdstd" align="center"><a href="https://books.google.com.sg/books?id=cxoCyF2DW30C&output=html_text&source=gbs_book_other_versions_r&cad=3" ><img alt="" class="coverthumb hover-card-attach-point" src="https://books.google.com.sg/books/content?id=cxoCyF2DW30C&printsec=frontcover&img=1&zoom=5" border="0" height="80"></a></td><td valign=top><div class=resbdy><a class="primary cresbdy" href="https://books.google.com.sg/books?id=cxoCyF2DW30C&output=html_text&source=gbs_book_other_versions_r&cad=3"><span dir=ltr>A Course on Group Theory</span></a><br><span style="line-height: 1.3em; font-size:-1;"><span><a href="https://www.google.com.sg/search?tbo=p&tbm=bks&q=inauthor:%22John+S.+Rose%22" class="secondary"><span dir=ltr>John S. Rose</span></a></span><br/><span><span style="color:#999">No preview available</span> - 1994</span><br/></span></div></td><td align=right></td></tr></table></div></div><script>(function () {var fn = window['_OC_WSBookList'] || window['_OC_BookList'];fn && fn('book_other_versions', [{"title":"A Course on Group Theory","authors":"John S. Rose","bib_key":"ISBN:9780486170664","pub_date":"27 May 2013","snippet":"Text for advanced courses in group theory focuses on finite groups, with emphasis on group actions. 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Chapters divided between normal and arithmetical structure of groups. 1978 edition.","subject":"Mathematics","info_url":"https://books.google.com.sg/books?id=pYk6AAAAIAAJ\u0026output=html_text\u0026source=gbs_book_other_versions","preview_url":"https://books.google.com.sg/books?id=pYk6AAAAIAAJ\u0026printsec=frontcover\u0026output=html_text\u0026source=gbs_book_other_versions","thumbnail_url":"https://books.google.com.sg/books/content?id=pYk6AAAAIAAJ\u0026printsec=frontcover\u0026img=1\u0026zoom=1\u0026edge=curl","num_pages":324,"viewability":2,"preview":"partial","embeddable":true,"my_ebooks_url":"https://www.google.com/accounts/Login?service=print\u0026continue=https://books.google.com.sg/books%3Fas_coll%3D7%26output%3Dhtml_text\u0026hl=en","has_scanned_text":true,"can_download_pdf":false,"can_download_epub":false,"is_pdf_drm_enabled":false,"is_epub_drm_enabled":false},{"title":"A Course on Group Theory","authors":"John S. Rose","bib_key":"ISBN:0486681947","pub_date":"1 Jan 1994","snippet":"Text for advanced courses in group theory focuses on finite groups, with emphasis on group actions. Explores normal and arithmetical structures of groups as well as ...","subject":"Mathematics","info_url":"https://books.google.com.sg/books?id=cxoCyF2DW30C\u0026output=html_text\u0026source=gbs_book_other_versions","preview_url":"https://books.google.com.sg/books?id=cxoCyF2DW30C\u0026output=html_text\u0026source=gbs_book_other_versions","thumbnail_url":"https://books.google.com.sg/books/content?id=cxoCyF2DW30C\u0026printsec=frontcover\u0026img=1\u0026zoom=1","num_pages":338,"viewability":4,"preview":"noview","embeddable":false,"my_ebooks_url":"https://www.google.com/accounts/Login?service=print\u0026continue=https://books.google.com.sg/books%3Fas_coll%3D7%26output%3Dhtml_text\u0026hl=en","can_download_pdf":false,"can_download_epub":false,"is_pdf_drm_enabled":false,"is_epub_drm_enabled":false}]);})();</script></div></div></div><div class=vertical_module_list_row><h3 class=about_title><a name="word_cloud_anchor"></a>Common terms and phrases</h3><div id=word_cloud class=about_content><div id=word_cloud_v><style type="text/css">.cloud9 {color: #7777cc;font-size: 10px;}.cloud8 {color: #6963CC;font-size: 10.5px;}.cloud7 {color: #6057CC;font-size: 11px;}.cloud6 {color: #574BCC;font-size: 11.5px;}.cloud5 {color: #4E3DCC;font-size: 12px;}.cloud4 {color: #4632CC;font-size: 14px;}.cloud3 {color: #3D26CC;font-size: 16px;}.cloud2 {color: #341ACC;font-size: 18px;}.cloud1 {color: #2B0DCC;font-size: 20px;}.cloud0 {color: #2200CC;font-size: 22px;}.cloud {margin-top: 4px;line-height: 24px;}.cloud a {margin-right: 6px;text-decoration: none;}.cloud a:hover {text-decoration: underline;}</style><div class=cloud><a href="https://books.google.com.sg/books?id=j-I7Zpq3GdIC&q=abelian+group&output=html_text&source=gbs_word_cloud_r&cad=4" class="cloud4"><span dir=ltr>abelian group</span></a> <a href="https://books.google.com.sg/books?id=j-I7Zpq3GdIC&q=action+of+G&output=html_text&source=gbs_word_cloud_r&cad=4" class="cloud5"><span dir=ltr>action of G</span></a> <a href="https://books.google.com.sg/books?id=j-I7Zpq3GdIC&q=argue+by+induction&output=html_text&source=gbs_word_cloud_r&cad=4" class="cloud8"><span dir=ltr>argue by induction</span></a> <a href="https://books.google.com.sg/books?id=j-I7Zpq3GdIC&q=Aut+G&output=html_text&source=gbs_word_cloud_r&cad=4" class="cloud6"><span dir=ltr>Aut G</span></a> <a href="https://books.google.com.sg/books?id=j-I7Zpq3GdIC&q=automorphism&output=html_text&source=gbs_word_cloud_r&cad=4" class="cloud7"><span dir=ltr>automorphism</span></a> <a href="https://books.google.com.sg/books?id=j-I7Zpq3GdIC&q=C%E2%82%82&output=html_text&source=gbs_word_cloud_r&cad=4" class="cloud6"><span dir=ltr>C₂</span></a> <a href="https://books.google.com.sg/books?id=j-I7Zpq3GdIC&q=CG(x&output=html_text&source=gbs_word_cloud_r&cad=4" class="cloud3"><span dir=ltr>CG(x</span></a> <a href="https://books.google.com.sg/books?id=j-I7Zpq3GdIC&q=characteristic+subgroup&output=html_text&source=gbs_word_cloud_r&cad=4" class="cloud3"><span dir=ltr>characteristic subgroup</span></a> <a href="https://books.google.com.sg/books?id=j-I7Zpq3GdIC&q=composition+series&output=html_text&source=gbs_word_cloud_r&cad=4" class="cloud1"><span dir=ltr>composition series</span></a> <a href="https://books.google.com.sg/books?id=j-I7Zpq3GdIC&q=conjugacy+class&output=html_text&source=gbs_word_cloud_r&cad=4" class="cloud2"><span dir=ltr>conjugacy class</span></a> <a href="https://books.google.com.sg/books?id=j-I7Zpq3GdIC&q=cyclic+group&output=html_text&source=gbs_word_cloud_r&cad=4" class="cloud3"><span dir=ltr>cyclic group</span></a> <a href="https://books.google.com.sg/books?id=j-I7Zpq3GdIC&q=defined&output=html_text&source=gbs_word_cloud_r&cad=4" class="cloud6"><span dir=ltr>defined</span></a> <a href="https://books.google.com.sg/books?id=j-I7Zpq3GdIC&q=definition&output=html_text&source=gbs_word_cloud_r&cad=4" class="cloud8"><span dir=ltr>definition</span></a> <a href="https://books.google.com.sg/books?id=j-I7Zpq3GdIC&q=denote&output=html_text&source=gbs_word_cloud_r&cad=4" class="cloud6"><span dir=ltr>denote</span></a> <a href="https://books.google.com.sg/books?id=j-I7Zpq3GdIC&q=direct+product&output=html_text&source=gbs_word_cloud_r&cad=4" class="cloud7"><span dir=ltr>direct product</span></a> <a href="https://books.google.com.sg/books?id=j-I7Zpq3GdIC&q=distinct+primes&output=html_text&source=gbs_word_cloud_r&cad=4" class="cloud8"><span dir=ltr>distinct primes</span></a> <a href="https://books.google.com.sg/books?id=j-I7Zpq3GdIC&q=element+of+G&output=html_text&source=gbs_word_cloud_r&cad=4" class="cloud6"><span dir=ltr>element of G</span></a> <a href="https://books.google.com.sg/books?id=j-I7Zpq3GdIC&q=factor+of+G&output=html_text&source=gbs_word_cloud_r&cad=4" class="cloud8"><span dir=ltr>factor of G</span></a> <a href="https://books.google.com.sg/books?id=j-I7Zpq3GdIC&q=finite+group&output=html_text&source=gbs_word_cloud_r&cad=4" class="cloud1"><span dir=ltr>finite group</span></a> <a href="https://books.google.com.sg/books?id=j-I7Zpq3GdIC&q=follows&output=html_text&source=gbs_word_cloud_r&cad=4" class="cloud8"><span dir=ltr>follows</span></a> <a href="https://books.google.com.sg/books?id=j-I7Zpq3GdIC&q=G+acts&output=html_text&source=gbs_word_cloud_r&cad=4" class="cloud8"><span dir=ltr>G acts</span></a> <a href="https://books.google.com.sg/books?id=j-I7Zpq3GdIC&q=G+is+finite&output=html_text&source=gbs_word_cloud_r&cad=4" class="cloud7"><span dir=ltr>G is finite</span></a> <a href="https://books.google.com.sg/books?id=j-I7Zpq3GdIC&q=G+is+nilpotent&output=html_text&source=gbs_word_cloud_r&cad=4" class="cloud7"><span dir=ltr>G is nilpotent</span></a> <a href="https://books.google.com.sg/books?id=j-I7Zpq3GdIC&q=G+is+soluble&output=html_text&source=gbs_word_cloud_r&cad=4" class="cloud7"><span dir=ltr>G is soluble</span></a> <a href="https://books.google.com.sg/books?id=j-I7Zpq3GdIC&q=G+of+order&output=html_text&source=gbs_word_cloud_r&cad=4" class="cloud7"><span dir=ltr>G of order</span></a> <a href="https://books.google.com.sg/books?id=j-I7Zpq3GdIC&q=G%E2%82%81&output=html_text&source=gbs_word_cloud_r&cad=4" class="cloud3"><span dir=ltr>G₁</span></a> <a href="https://books.google.com.sg/books?id=j-I7Zpq3GdIC&q=G%E2%82%82&output=html_text&source=gbs_word_cloud_r&cad=4" class="cloud6"><span dir=ltr>G₂</span></a> <a href="https://books.google.com.sg/books?id=j-I7Zpq3GdIC&q=group+G&output=html_text&source=gbs_word_cloud_r&cad=4" class="cloud3"><span dir=ltr>group G</span></a> <a href="https://books.google.com.sg/books?id=j-I7Zpq3GdIC&q=group+of+order&output=html_text&source=gbs_word_cloud_r&cad=4" class="cloud5"><span dir=ltr>group of order</span></a> <a href="https://books.google.com.sg/books?id=j-I7Zpq3GdIC&q=H+in+G&output=html_text&source=gbs_word_cloud_r&cad=4" class="cloud5"><span dir=ltr>H in G</span></a> <a href="https://books.google.com.sg/books?id=j-I7Zpq3GdIC&q=H%E2%82%81&output=html_text&source=gbs_word_cloud_r&cad=4" class="cloud4"><span dir=ltr>H₁</span></a> <a href="https://books.google.com.sg/books?id=j-I7Zpq3GdIC&q=H%E2%82%82&output=html_text&source=gbs_word_cloud_r&cad=4" class="cloud7"><span dir=ltr>H₂</span></a> <a href="https://books.google.com.sg/books?id=j-I7Zpq3GdIC&q=Hall+subgroup&output=html_text&source=gbs_word_cloud_r&cad=4" class="cloud3"><span dir=ltr>Hall subgroup</span></a> <a href="https://books.google.com.sg/books?id=j-I7Zpq3GdIC&q=Hence&output=html_text&source=gbs_word_cloud_r&cad=4" class="cloud4"><span dir=ltr>Hence</span></a> <a href="https://books.google.com.sg/books?id=j-I7Zpq3GdIC&q=Hint&output=html_text&source=gbs_word_cloud_r&cad=4" class="cloud4"><span dir=ltr>Hint</span></a> <a href="https://books.google.com.sg/books?id=j-I7Zpq3GdIC&q=homomorphism&output=html_text&source=gbs_word_cloud_r&cad=4" class="cloud3"><span dir=ltr>homomorphism</span></a> <a href="https://books.google.com.sg/books?id=j-I7Zpq3GdIC&q=identity+element&output=html_text&source=gbs_word_cloud_r&cad=4" class="cloud8"><span dir=ltr>identity element</span></a> <a href="https://books.google.com.sg/books?id=j-I7Zpq3GdIC&q=infinite&output=html_text&source=gbs_word_cloud_r&cad=4" class="cloud7"><span dir=ltr>infinite</span></a> <a href="https://books.google.com.sg/books?id=j-I7Zpq3GdIC&q=involution&output=html_text&source=gbs_word_cloud_r&cad=4" class="cloud7"><span dir=ltr>involution</span></a> <a href="https://books.google.com.sg/books?id=j-I7Zpq3GdIC&q=isomorphic&output=html_text&source=gbs_word_cloud_r&cad=4" class="cloud3"><span dir=ltr>isomorphic</span></a> <a href="https://books.google.com.sg/books?id=j-I7Zpq3GdIC&q=K%E2%82%81&output=html_text&source=gbs_word_cloud_r&cad=4" class="cloud5"><span dir=ltr>K₁</span></a> <a href="https://books.google.com.sg/books?id=j-I7Zpq3GdIC&q=Lemma&output=html_text&source=gbs_word_cloud_r&cad=4" class="cloud7"><span dir=ltr>Lemma</span></a> <a href="https://books.google.com.sg/books?id=j-I7Zpq3GdIC&q=Let+G&output=html_text&source=gbs_word_cloud_r&cad=4" class="cloud1"><span dir=ltr>Let G</span></a> <a href="https://books.google.com.sg/books?id=j-I7Zpq3GdIC&q=Let+H&output=html_text&source=gbs_word_cloud_r&cad=4" class="cloud5"><span dir=ltr>Let H</span></a> <a href="https://books.google.com.sg/books?id=j-I7Zpq3GdIC&q=Math&output=html_text&source=gbs_word_cloud_r&cad=4" class="cloud8"><span dir=ltr>Math</span></a> <a href="https://books.google.com.sg/books?id=j-I7Zpq3GdIC&q=maximal+subgroup&output=html_text&source=gbs_word_cloud_r&cad=4" class="cloud2"><span dir=ltr>maximal subgroup</span></a> <a href="https://books.google.com.sg/books?id=j-I7Zpq3GdIC&q=minimal+normal+subgroup&output=html_text&source=gbs_word_cloud_r&cad=4" class="cloud2"><span dir=ltr>minimal normal subgroup</span></a> <a href="https://books.google.com.sg/books?id=j-I7Zpq3GdIC&q=n%E2%82%81&output=html_text&source=gbs_word_cloud_r&cad=4" class="cloud7"><span dir=ltr>n₁</span></a> <a href="https://books.google.com.sg/books?id=j-I7Zpq3GdIC&q=normal+in+G&output=html_text&source=gbs_word_cloud_r&cad=4" class="cloud7"><span dir=ltr>normal in G</span></a> <a href="https://books.google.com.sg/books?id=j-I7Zpq3GdIC&q=p-group&output=html_text&source=gbs_word_cloud_r&cad=4" class="cloud0"><span dir=ltr>p-group</span></a> <a href="https://books.google.com.sg/books?id=j-I7Zpq3GdIC&q=P%E2%82%81&output=html_text&source=gbs_word_cloud_r&cad=4" class="cloud8"><span dir=ltr>P₁</span></a> <a href="https://books.google.com.sg/books?id=j-I7Zpq3GdIC&q=permutation&output=html_text&source=gbs_word_cloud_r&cad=4" class="cloud8"><span dir=ltr>permutation</span></a> <a href="https://books.google.com.sg/books?id=j-I7Zpq3GdIC&q=positive+integer&output=html_text&source=gbs_word_cloud_r&cad=4" class="cloud3"><span dir=ltr>positive integer</span></a> <a href="https://books.google.com.sg/books?id=j-I7Zpq3GdIC&q=prime+divisor&output=html_text&source=gbs_word_cloud_r&cad=4" class="cloud7"><span dir=ltr>prime divisor</span></a> <a href="https://books.google.com.sg/books?id=j-I7Zpq3GdIC&q=Proof&output=html_text&source=gbs_word_cloud_r&cad=4" class="cloud5"><span dir=ltr>Proof</span></a> <a href="https://books.google.com.sg/books?id=j-I7Zpq3GdIC&q=proper+subgroup&output=html_text&source=gbs_word_cloud_r&cad=4" class="cloud7"><span dir=ltr>proper subgroup</span></a> <a href="https://books.google.com.sg/books?id=j-I7Zpq3GdIC&q=prove&output=html_text&source=gbs_word_cloud_r&cad=4" class="cloud7"><span dir=ltr>prove</span></a> <a href="https://books.google.com.sg/books?id=j-I7Zpq3GdIC&q=quotient+group&output=html_text&source=gbs_word_cloud_r&cad=4" class="cloud2"><span dir=ltr>quotient group</span></a> <a href="https://books.google.com.sg/books?id=j-I7Zpq3GdIC&q=series+of+G&output=html_text&source=gbs_word_cloud_r&cad=4" class="cloud5"><span dir=ltr>series of G</span></a> <a href="https://books.google.com.sg/books?id=j-I7Zpq3GdIC&q=soluble+group&output=html_text&source=gbs_word_cloud_r&cad=4" class="cloud3"><span dir=ltr>soluble group</span></a> <a href="https://books.google.com.sg/books?id=j-I7Zpq3GdIC&q=subgroup+H&output=html_text&source=gbs_word_cloud_r&cad=4" class="cloud6"><span dir=ltr>subgroup H</span></a> <a href="https://books.google.com.sg/books?id=j-I7Zpq3GdIC&q=subgroup+of+G&output=html_text&source=gbs_word_cloud_r&cad=4" class="cloud0"><span dir=ltr>subgroup of G</span></a> <a href="https://books.google.com.sg/books?id=j-I7Zpq3GdIC&q=subgroup+of+index&output=html_text&source=gbs_word_cloud_r&cad=4" class="cloud8"><span dir=ltr>subgroup of index</span></a> <a href="https://books.google.com.sg/books?id=j-I7Zpq3GdIC&q=subgroup+of+order&output=html_text&source=gbs_word_cloud_r&cad=4" class="cloud8"><span dir=ltr>subgroup of order</span></a> <a href="https://books.google.com.sg/books?id=j-I7Zpq3GdIC&q=subnormal+in+G&output=html_text&source=gbs_word_cloud_r&cad=4" class="cloud7"><span dir=ltr>subnormal in G</span></a> <a href="https://books.google.com.sg/books?id=j-I7Zpq3GdIC&q=subnormal+subgroup&output=html_text&source=gbs_word_cloud_r&cad=4" class="cloud2"><span dir=ltr>subnormal subgroup</span></a> <a href="https://books.google.com.sg/books?id=j-I7Zpq3GdIC&q=Suppose+that+G&output=html_text&source=gbs_word_cloud_r&cad=4" class="cloud3"><span dir=ltr>Suppose that G</span></a> <a href="https://books.google.com.sg/books?id=j-I7Zpq3GdIC&q=Sylow+p-subgroup&output=html_text&source=gbs_word_cloud_r&cad=4" class="cloud0"><span dir=ltr>Sylow p-subgroup</span></a> <a href="https://books.google.com.sg/books?id=j-I7Zpq3GdIC&q=Sylow%27s+theorem&output=html_text&source=gbs_word_cloud_r&cad=4" class="cloud8"><span dir=ltr>Sylow's theorem</span></a> <a href="https://books.google.com.sg/books?id=j-I7Zpq3GdIC&q=transversal+to+H&output=html_text&source=gbs_word_cloud_r&cad=4" class="cloud8"><span dir=ltr>transversal to H</span></a> <a href="https://books.google.com.sg/books?id=j-I7Zpq3GdIC&q=trivial&output=html_text&source=gbs_word_cloud_r&cad=4" class="cloud8"><span dir=ltr>trivial</span></a> <a href="https://books.google.com.sg/books?id=j-I7Zpq3GdIC&q=vector+space&output=html_text&source=gbs_word_cloud_r&cad=4" class="cloud8"><span dir=ltr>vector space</span></a> <a href="https://books.google.com.sg/books?id=j-I7Zpq3GdIC&q=wreath+product&output=html_text&source=gbs_word_cloud_r&cad=4" class="cloud3"><span dir=ltr>wreath product</span></a></div></div></div></div><div class=vertical_module_list_row><h3 class=about_title><a name="about_author_anchor"></a>About the author <span style="color:#666; font-weight:normal">(1994)</span></h3><div id=about_author class=about_content><div id=about_author_v><div class=textmodulecontent>The late John S. Rose was Senior Lecturer in Pure Mathematics at England's University of Newcastle upon Tyne. </div></div></div></div><div class=vertical_module_list_row><h3 class="about_title">Bibliographic information</h3><div class="about_content" id="metadata_content" style="padding-bottom:.3em"><div class="metadata_sectionwrap"><table id="metadata_content_table"><tr class="metadata_row"><td class="metadata_label">Title</td><td class="metadata_value"><span dir=ltr>A Course on Group Theory</span><br><a class="primary" href="https://www.google.com.sg/search?tbo=p&tbm=bks&q=bibliogroup:%22A+course+on+group+theory%22&source=gbs_metadata_r&cad=6"><i><span dir=ltr>A course on group theory</span></i></a><br><a class="primary" href="https://www.google.com.sg/search?tbo=p&tbm=bks&q=bibliogroup:%22Dover+Books+on+Mathematics+Series%22&source=gbs_metadata_r&cad=6"><i><span dir=ltr>Dover Books on Mathematics Series</span></i></a><br><a class="primary" href="https://www.google.com.sg/search?tbo=p&tbm=bks&q=bibliogroup:%22Dover+books+on+advanced+mathematics%22&source=gbs_metadata_r&cad=6"><i><span dir=ltr>Dover books on advanced mathematics</span></i></a><br><a class="primary" href="https://www.google.com.sg/search?tbo=p&tbm=bks&q=bibliogroup:%22Dover+books+on+astronomy+and+astrophysics%22&source=gbs_metadata_r&cad=6"><i><span dir=ltr>Dover books on astronomy and astrophysics</span></i></a><br><a class="primary" href="https://www.google.com.sg/search?tbo=p&tbm=bks&q=bibliogroup:%22Phoenix+Edition+Series%22&source=gbs_metadata_r&cad=6"><i><span dir=ltr>Phoenix Edition Series</span></i></a></td></tr><tr class="metadata_row"><td class="metadata_label"><span dir=ltr>Author</span></td><td class="metadata_value"><a class="primary" href="https://www.google.com.sg/search?tbo=p&tbm=bks&q=inauthor:%22John+S.+Rose%22&source=gbs_metadata_r&cad=6"><span dir=ltr>John S. Rose</span></a></td></tr><tr class="metadata_row"><td class="metadata_label"><span dir=ltr>Edition</span></td><td class="metadata_value"><span dir=ltr>illustrated, unabridged, reprint, revised</span></td></tr><tr class="metadata_row"><td class="metadata_label"><span dir=ltr>Publisher</span></td><td class="metadata_value"><span dir=ltr>Courier Corporation, 1994</span></td></tr><tr class="metadata_row"><td class="metadata_label"><span dir=ltr>ISBN</span></td><td class="metadata_value"><span dir=ltr>0486681947, 9780486681948</span></td></tr><tr class="metadata_row"><td class="metadata_label"><span dir=ltr>Length</span></td><td class="metadata_value"><span dir=ltr>310 pages</span></td></tr><tr class="metadata_row"><td class="metadata_label"><span dir=ltr>Subjects</span></td><td class="metadata_value"><div style="display:inline" itemscope itemtype="http://data-vocabulary.org/Breadcrumb"><a class="primary" href="https://www.google.com.sg/search?tbo=p&tbm=bks&q=subject:%22Mathematics%22" itemprop="url" dir=ltr><span itemprop="title">Mathematics</span></a></div> › <div style="display:inline" itemscope itemtype="http://data-vocabulary.org/Breadcrumb"><a class="primary" href="https://www.google.com.sg/search?tbo=p&tbm=bks&q=subject:%22Mathematics+Group+Theory%22" itemprop="url" dir=ltr><span itemprop="title">Group Theory</span></a></div><br><br><a class="primary" href="https://www.google.com.sg/search?tbo=p&tbm=bks&q=subject:%22Mathematics+/+Group+Theory%22&source=gbs_metadata_r&cad=6"><span dir=ltr>Mathematics / Group Theory</span></a></td></tr><tr class="metadata_row"><td>&nbsp</td><td>&nbsp</td></tr><tr class="metadata_row"><td class="metadata_label"><span dir=ltr>Export Citation</span></td><td class="metadata_value"><a class="gb-button " href="https://books.google.com.sg/books/download/A_Course_on_Group_Theory.bibtex?id=j-I7Zpq3GdIC&output=bibtex"><span dir=ltr>BiBTeX</span></a> <a class="gb-button " href="https://books.google.com.sg/books/download/A_Course_on_Group_Theory.enw?id=j-I7Zpq3GdIC&output=enw"><span dir=ltr>EndNote</span></a> <a class="gb-button " href="https://books.google.com.sg/books/download/A_Course_on_Group_Theory.ris?id=j-I7Zpq3GdIC&output=ris"><span dir=ltr>RefMan</span></a></td></tr></table></div><div style="clear:both"></div></div></div><div id="footer_table" style="font-size:83%;text-align:center;position:relative;top:20px;height:4.5em;margin-top:2em"><div style="margin-bottom:8px"><a href="/intl/en/googlebooks/about.html"><nobr><nobr>About Google Books</nobr></nobr></a> - <a href="/intl/en/googlebooks/privacy.html"><nobr><nobr>Privacy Policy</nobr></nobr></a> - <a href="/intl/en/googlebooks/tos.html"><nobr><nobr>Terms of Service</nobr></nobr></a> - <a href="http://books.google.com.sg/support/partner/?hl=en-SG"><nobr><nobr>Information for Publishers</nobr></nobr></a> - <a href="http://books.google.com.sg/support/answer/180577?hl=en-SG&url=https://books.google.com.sg/books?id=j-I7Zpq3GdIC&redir_esc=y&hl=en&output=html_text&v=j-I7Zpq3GdIC&is=atb"><nobr><nobr>Report an issue</nobr></nobr></a> - <a href="http://books.google.com.sg/support/topic/4359341?hl=en-SG"><nobr><nobr>Help</nobr></nobr></a> - <a href="https://www.google.com.sg/"><nobr><nobr>Google Home</nobr></nobr></a></div></div></div></div></div><script>(function() {var href = window.location.href;if (href.indexOf('?') !== -1) {var parameters = href.split('?')[1].split('&');for (var i = 0; i < parameters.length; i++) {var param = parameters[i].split('=');if (param[0] == 'focus') {var elem = document.getElementById(param[1]);if (elem) {elem.focus();}}}}})();</script>