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Published by EMS Press"/><meta property="og:image" content="https://content.ems.press/assets/public/images/books/cover-67.png"/><link rel="canonical" href="https://ems.press/books/elm/67"/><meta name="citation_title" content="Finite Generalized Quadrangles"/><meta name="citation_author" content="Stanley E. Payne"/><meta name="citation_author" content="Joseph A. Thas"/><meta name="citation_publication_date" content="2009/04/08"/><meta name="citation_issn" content="2523-5176"/><meta name="citation_issn" content="2523-5184"/><meta name="citation_isbn" content="978-3-03719-066-1"/><meta name="citation_isbn" content="978-3-03719-566-6"/><meta name="citation_doi" content="10.4171/066"/><meta name="citation_pdf_url" content="https://ems.press/content/book-files/19914"/><script type="application/ld+json">{"@context":"https://schema.org","@type":["Product","Book"],"name":"Finite Generalized Quadrangles","description":"Generalized quadrangles (GQ) were formally introduced by J. Tits in 1959 in order to describe geometric properties of simple groups of Lie type of rank 2. After its appearance in 1984, _Finite Generalized Quadrangles_ (FGQ) quickly became the standard reference for finite GQ. It presents the whole story of the subject from the very beginning in a book of modest length.\n\nThis second edition is essentially a reprint of the first edition. It is a careful rendering into LaTeX of the original, along with an appendix that introduces major new results pertaining to GQ, especially in those areas in which the authors of this work have made a contribution.\n\nThe first edition has been out of print for many years, and the new edition makes again available this classical reference in the rapidly increasing field of finite geometries.","image":"https://content.ems.press/assets/public/images/books/cover-67.png","isbn":"978-3-03719-066-1","offers":[{"@type":"Offer","price":"49.00","priceCurrency":"EUR","availability":"InStock"},{"@type":"Offer","price":"53.00","priceCurrency":"USD","availability":"InStock"},{"@type":"Offer","price":"49.00","priceCurrency":"EUR","availability":"InStock"},{"@type":"Offer","price":"53.00","priceCurrency":"USD","availability":"InStock"}]}</script><link rel="preload" as="image" imageSrcSet="/_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fbooks%2Fcover-67.png&w=256&q=90 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Payne</h3><span class="jsx-2177874377 organisation">University of Colorado Denver, Denver, USA</span></header></section></li><li class="jsx-2097570476 list-item"><section class="jsx-2177874377 person"><header class="jsx-2177874377 title-wrapper"><h3 class="jsx-2177874377 title">Joseph A. Thas</h3><span class="jsx-2177874377 organisation">Ghent University, Ghent, Belgium</span></header></section></li></ul></div></div></div><nav class="jsx-2370296075 tab-navigation tab-navigation "><ul class="jsx-2370296075 list"><li class="jsx-2370296075"><a class="link active jsx-2462825770" href="/books/elm/67"><svg class="stripes" xmlns="http://www.w3.org/2000/svg" width="70" viewBox="0 0 70 27"><g><rect x="0" y="0" width="100%" height="9" fill="#FDB913"></rect><rect x="0" y="18" width="100%" height="9" fill="#FDB913"></rect></g></svg>Overview</a></li><li class="jsx-2370296075"><a class="link jsx-2462825770" href="/books/elm/67/contents">Contents</a></li><li class="jsx-2370296075"><a class="link jsx-2462825770" href="/books/elm/67/reviews">Reviews</a></li></ul></nav><div class="jsx-310690786 jsx-2857661604 cover"><img alt="Finite Generalized Quadrangles cover" fetchpriority="high" width="2008" height="2835" decoding="async" data-nimg="1" style="color:transparent;width:100%;height:auto" sizes="33vw" srcSet="/_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fbooks%2Fcover-67.png&w=256&q=90 256w, /_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fbooks%2Fcover-67.png&w=384&q=90 384w, /_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fbooks%2Fcover-67.png&w=640&q=90 640w, /_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fbooks%2Fcover-67.png&w=750&q=90 750w, /_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fbooks%2Fcover-67.png&w=828&q=90 828w, /_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fbooks%2Fcover-67.png&w=1080&q=90 1080w, /_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fbooks%2Fcover-67.png&w=1200&q=90 1200w, /_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fbooks%2Fcover-67.png&w=1920&q=90 1920w, /_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fbooks%2Fcover-67.png&w=2048&q=90 2048w, /_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fbooks%2Fcover-67.png&w=3840&q=90 3840w" src="/_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fbooks%2Fcover-67.png&w=3840&q=90"/><div class="jsx-310690786 jsx-2857661604 actions"><div class="jsx-3326522818 book-actions"><div class="jsx-3326522818 buttons"><a class="button buy-button jsx-1368592022 jsx-2462825770" href="/books/elm/67/buy">Buy from <strong class="jsx-3326522818 price">€49.00</strong></a><a class="button jsx-1554637200 download-button jsx-2661684887 jsx-2462825770" href="/content/book-files/19914?nt=1">Download PDF</a></div><div class="jsx-3326522818 access-info"><p class="jsx-1012291113">A subscription is required to access this book.</p></div></div></div></div><main style="grid-area:main;margin-top:1.8rem"><p>Generalized quadrangles (GQ) were formally introduced by J. Tits in 1959 in order to describe geometric properties of simple groups of Lie type of rank 2. After its appearance in 1984, <em>Finite Generalized Quadrangles</em> (FGQ) quickly became the standard reference for finite GQ. It presents the whole story of the subject from the very beginning in a book of modest length.</p> <p>This second edition is essentially a reprint of the first edition. It is a careful rendering into LaTeX of the original, along with an appendix that introduces major new results pertaining to GQ, especially in those areas in which the authors of this work have made a contribution.</p> <p>The first edition has been out of print for many years, and the new edition makes again available this classical reference in the rapidly increasing field of finite geometries.</p></main><aside class="jsx-1279956873 jsx-1604905398 metadata-box"><h2 class="jsx-1279956873 jsx-1604905398">Dates</h2><dl class="jsx-1279956873 jsx-1604905398"><dt class="jsx-1279956873 jsx-1604905398">Published</dt><dd class="jsx-1279956873 jsx-1604905398">8 April 2009</dd></dl><h2 class="jsx-1279956873 jsx-1604905398">Identifiers</h2><dl class="jsx-1279956873 jsx-1604905398"><dt class="jsx-1279956873 jsx-1604905398">DOI</dt><dd class="jsx-1279956873 jsx-1604905398"><a href="https://doi.org/10.4171/066" class="jsx-1279956873 jsx-1604905398">10.4171/066</a></dd><dt class="jsx-1279956873 jsx-1604905398">ISBN print</dt><dd class="jsx-1279956873 jsx-1604905398">978-3-03719-066-1</dd><dt class="jsx-1279956873 jsx-1604905398">ISBN digital</dt><dd class="jsx-1279956873 jsx-1604905398">978-3-03719-566-6</dd></dl><h2 class="jsx-1279956873 jsx-1604905398">Keywords</h2><ul class="jsx-1279956873 jsx-1604905398 keywords"><li class="jsx-1279956873 jsx-1604905398">Finite generalized quadrangle</li><li class="jsx-1279956873 jsx-1604905398">finite projective space</li><li class="jsx-1279956873 jsx-1604905398">generalized polygon</li><li class="jsx-1279956873 jsx-1604905398">polar space</li><li class="jsx-1279956873 jsx-1604905398">incidence geometry</li><li class="jsx-1279956873 jsx-1604905398">circle geometry</li></ul><h2 class="jsx-1279956873 jsx-1604905398">Mathematics Subject Classification</h2><ul class="jsx-1279956873 jsx-1604905398 keywords"><li class="jsx-1279956873 jsx-1604905398">05-02</li><li class="jsx-1279956873 jsx-1604905398">51-02</li><li class="jsx-1279956873 jsx-1604905398">05B05</li><li class="jsx-1279956873 jsx-1604905398">05B25</li><li class="jsx-1279956873 jsx-1604905398">51B10</li><li class="jsx-1279956873 jsx-1604905398">51B15</li><li class="jsx-1279956873 jsx-1604905398">51B20</li><li class="jsx-1279956873 jsx-1604905398">51E05</li><li class="jsx-1279956873 jsx-1604905398">51E12</li><li class="jsx-1279956873 jsx-1604905398">51E14</li><li class="jsx-1279956873 jsx-1604905398">51E20</li><li class="jsx-1279956873 jsx-1604905398">51E21</li><li class="jsx-1279956873 jsx-1604905398">51E30</li></ul><h2 class="jsx-1279956873 jsx-1604905398">Print</h2><p class="jsx-1279956873 jsx-1604905398">Softcover, 299 pages, 17cm x 24cm</p><p class="jsx-1279956873 jsx-1604905398 copyright">© EMS Press</p></aside></div></article></main><footer class="jsx-812847572 footer"><div class="jsx-812847572 inner layout-container"><nav title="Footer Navigation" class="jsx-812847572"><ul class="jsx-812847572"><li class="jsx-812847572"><a class="jsx-2462825770 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Society.</p></div></footer></div></div><script id="__NEXT_DATA__" type="application/json">{"props":{"pageProps":{"error":false,"data":{"baseUrl":"https://ems.press","emsSocietyUrl":"https://euromathsoc.org/","requiredConsentVersion":2,"sentryDSN":"https://c18d3379cdda4e76b7b57ad1c555d51c@o1351767.ingest.sentry.io/6634446","sentryEnabled":true,"sentryEnvironment":"production","googleAnalyticsMeasurementID":"G-FR28GMJ82P","isMultiVolumeChild":false,"book":{"type":"books","id":"67","titleTex":"Finite Generalized Quadrangles","subtitleTex":"Second Edition","doi":"10.4171/066","isbn":"978-3-03719-066-1","eIsbn":"978-3-03719-566-6","bookType":"monograph","copyright":"© EMS Press","publishedAt":"2009-04-08T00:00:00.000Z","binding":"softcover","pages":299,"printWidthCm":17,"printHeightCm":24,"keywords":["Finite generalized quadrangle","finite projective space","generalized polygon","polar space","incidence geometry","circle 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Tits in 1959 in order to describe geometric properties of simple groups of Lie type of rank 2. After its appearance in 1984, _Finite Generalized Quadrangles_ (FGQ) quickly became the standard reference for finite GQ. It presents the whole story of the subject from the very beginning in a book of modest length.\n\nThis second edition is essentially a reprint of the first edition. It is a careful rendering into LaTeX of the original, along with an appendix that introduces major new results pertaining to GQ, especially in those areas in which the authors of this work have made a contribution.\n\nThe first edition has been out of print for many years, and the new edition makes again available this classical reference in the rapidly increasing field of finite geometries.","coverImage":{"data":{"type":"images","id":"19890","width":2008,"height":2835,"url":"https://content.ems.press/assets/public/images/books/cover-67.png"}},"bookFiles":{"data":[{"type":"book-files","id":"19914","createdAt":"2022-04-20T08:56:14.872Z","updatedAt":"2022-04-20T08:56:14.872Z","contentType":"application/pdf","path":"full-texts/books/67/online-pdf/978-3-03719-566-6.pdf","sizeBytes":2356782,"md5":"4d3997c0af3bfa1253704042e09b49e1","sha256":"84867641ccf70eb503e4d520409565fc27a2828d3a9859b000e4a94f64bf34dc","fileType":"full-text-online-pdf","publishedAt":"2009-04-08T00:00:00.000Z","publishedAtPrecision":"day","access":false},{"type":"book-files","id":"19915","createdAt":"2022-04-20T08:56:14.872Z","updatedAt":"2022-04-20T08:56:14.872Z","contentType":"application/pdf","path":"full-texts/books/67/supplementary-files/9783037190661_preface.pdf","sizeBytes":61209,"md5":"b4e789d6334bf839aca07fa6c9494383","sha256":"7541454311aa52be05e4daed650870a09b752b9ce954130ed8f3aba2ca062bbe","fileType":"supplementary-book-preface","publishedAt":"2009-04-08T00:00:00.000Z","publishedAtPrecision":"day","description":"Preface","access":true,"url":"https://content.ems.press/assets/public/full-texts/books/67/supplementary-files/9783037190661_preface.pdf"},{"type":"book-files","id":"19916","createdAt":"2022-04-20T08:56:14.872Z","updatedAt":"2022-04-20T08:56:14.872Z","contentType":"application/pdf","path":"full-texts/books/67/supplementary-files/9783037190661_contents.pdf","sizeBytes":94658,"md5":"d3fe8c26087cec075e2c14a324ddaecd","sha256":"c3a0ecff5bf76f37ebf2eada7e00037ea54b6d21934de8777af27a0ae0e07e7e","fileType":"supplementary-book-table-of-contents","publishedAt":"2009-04-08T00:00:00.000Z","publishedAtPrecision":"day","description":"Table of Contents","access":true,"url":"https://content.ems.press/assets/public/full-texts/books/67/supplementary-files/9783037190661_contents.pdf"},{"type":"book-files","id":"19917","createdAt":"2022-04-20T08:56:14.872Z","updatedAt":"2022-04-20T08:56:14.872Z","contentType":"application/pdf","path":"full-texts/books/67/supplementary-files/Review in MR 2508121.pdf","sizeBytes":119547,"md5":"7e4c40a9dc84e5f04a00695cf515633f","sha256":"4f34f1fa42263ba123352878d425b490a286845828a31a7ec20313093ae91b96","fileType":"supplementary-book-review","publishedAt":"2009-04-08T00:00:00.000Z","publishedAtPrecision":"day","description":"Review in MR 2508121","access":true,"url":"https://content.ems.press/assets/public/full-texts/books/67/supplementary-files/Review in MR 2508121.pdf"}]},"bookSeries":{"data":{"type":"book-series","id":"3","code":"elm","issn":"2523-5176","eIssn":"2523-5184","name":"EMS Series of Lectures in Mathematics"}},"bookSupplementaryUrls":{"data":[{"type":"book-supplementary-urls","id":"121","createdAt":"2023-02-13T14:34:37.187Z","updatedAt":"2023-02-13T14:34:37.204Z","title":"Review in Zentralblatt MATH 05363282","url":"http://www.zentralblatt-math.org/zmath/en/search/?q=an:pre05363282\u0026format=complete","urlType":"review"}]},"multiVolumeParent":{"data":null},"personGroups":{"data":[{"type":"person-groups","id":"17114","name":"Authors","groupType":"authors","members":{"data":[{"type":"person-group-members","id":"10347147","name":"Stanley E. 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