Document Zbl 07877988

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Algebra</a> <a href="/?q=in%3A514891" title="Articles in this Issue">656, 77-117 (2024)</a>. </div> <div class="abstract">The authors study topological group theoretic properties of algebraic groups over local fields, including the study of groups of this kind that are minimal (i.e., admit no weaker (Hausdorff) group topology). In particular, the authors found conditions under which these groups are scaled (i.e., have closed images under arbitrary continuous homomorphisms into arbitrary Hausdorff topological groups).<div class="reviewer"> Reviewer: <a href="/authors/?q=rv%3A11003">Alexander Isaakovich Shtern (Moskva)</a></div> <div class="clearfix"></div></div> <div class="clear"></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A20G25" title="MSC2020">20G25</a> </td> <td class="space"> Linear algebraic groups over local fields and their integers </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A22E50" title="MSC2020">22E50</a> </td> <td class="space"> Representations of Lie and linear algebraic groups over local fields </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A22A10" title="MSC2020">22A10</a> </td> <td class="space"> Analysis on general topological groups </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Aalgebraic+groups">algebraic groups</a>; <a href="/?q=ut%3Atopological+groups">topological groups</a>; <a href="/?q=ut%3Aminimal+groups">minimal groups</a>; <a href="/?q=ut%3ALie+groups">Lie groups</a></div>  <div class="modal fade" id="metadataModal" tabindex="-1" role="dialog" aria-labelledby="myModalLabel"> <div class="modal-dialog" role="document"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button> <h4 class="modal-title" id="myModalLabel">Cite</h4> </div> <div class="modal-body"> <div class="form-group"> <label for="select-output" class="control-label">Format</label> <select id="select-output" class="form-control" aria-label="Select Metadata format"></select> </div> <div class="form-group"> <label for="metadataText" class="control-label">Result</label> <textarea class="form-control" id="metadataText" rows="10" style="min-width: 100%;max-width: 100%"></textarea> </div> <div id="metadata-alert" class="alert alert-danger" role="alert" style="display: none;">  </div> </div> <div class="modal-footer"> <button type="button" class="btn btn-primary" onclick="copyMetadata()">Copy to clipboard</button> <button type="button" class="btn btn-default" data-dismiss="modal">Close</button> </div> </div> </div> </div> <div class="functions clearfix"> <div class="function">  <a type="button" class="btn btn-default btn-xs pdf" data-toggle="modal" data-target="#metadataModal" data-itemtype="Zbl" data-itemname="Zbl 07877988" data-ciurl="/ci/07877988" data-biburl="/bibtex/07877988.bib" data-amsurl="/amsrefs/07877988.bib" data-xmlurl="/xml/07877988.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07877988.pdf" title="Zbl 07877988 as PDF">Review PDF</a> </div> <div class="fulltexts"> <span class="fulltext">Full Text:</span> <a class="btn btn-default btn-xs" type="button" href="https://doi.org/10.1016/j.jalgebra.2023.09.001" aria-label="DOI for “Homomorphic images of algebraic groups”" title="10.1016/j.jalgebra.2023.09.001">DOI</a> <a class="btn btn-default btn-xs" type="button" href="https://arxiv.org/abs/2212.03055"title="Note: arXiv document may differ from published version">arXiv</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">Banakh, Taras, Categorically closed topological groups, Axioms, 6, 3, 23, 2017 · <a href="/1422.22008" class="nowrap">Zbl 1422.22008</a></td> </tr><tr> <td>[2]</td> <td class="space">Bader, Uri; Duchesne, Bruno; Lécureux, Jean, Almost algebraic actions of algebraic groups and applications to algebraic representations, Groups Geom. 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Mat., 10, 6, 513-528, 1946 · <a href="/0061.04206" class="nowrap">Zbl 0061.04206</a></td> </tr><tr> <td>[28]</td> <td class="space">Serre, Jean-Pierre, Lie Algebras and Lie Groups: 1964 Lectures Given at Harvard University, 2009, Springer · <a href="/0132.27803" class="nowrap">Zbl 0132.27803</a></td> </tr><tr> <td>[29]</td> <td class="space">Shlossberg, Menachem, Minimality conditions equivalent to the finitude of fermat and mersenne primes, 2022, arXiv preprint</td> </tr><tr> <td>[30]</td> <td class="space">Weil, André, Basic Number Theory, Classics in Mathematics, 1995, Springer-Verlag: Springer-Verlag Berlin, Reprint of the second (1973) edition · <a href="/0823.11001" class="nowrap">Zbl 0823.11001</a></td> </tr></table> <div class="reference_disclaimer"> This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching. </div> </div></article> </div></div> </div> </div> <div class="clearfix"></div> </div> </div> <div id="foot"><div class="copyright"> © 2025 <a target="fiz" href="https://www.fiz-karlsruhe.de/en">FIZ Karlsruhe GmbH</a> <a href="/privacy-policy/">Privacy Policy</a> <a href="/legal-notices/">Legal Notices</a> <a href="/terms-conditions/">Terms & Conditions</a> <div class="info"> <ul class="nav"> <li class="mastodon"> <a href="https://mathstodon.xyz/@zbMATH" target="_blank" class="no-new-tab-icon"> <img src="/static/mastodon.png" title="zbMATH at Mathstodon (opens in new tab)" alt="Mastodon logo"> </a> </li> </ul> </div> </div> <div class="clearfix" style="height: 0px;"></div> </div> </div> <script src="https://static.zbmath.org/contrib/jquery/1.9.1/jquery.min.js"></script> <script src="https://static.zbmath.org/contrib/jquery-caret/1.5.2/jquery.caret.min.js"></script> <script src="/static/js/jquery-ui-1.10.1.custom.min.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap/v3.3.7zb1/js/bootstrap.min.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap-lightbox/v0.7.0/bootstrap-lightbox.min.js"></script> <script src="https://static.zbmath.org/contrib/retina/unknown/retina.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap-select/v1.13.14/js/bootstrap-select.min.js"></script> <script> var SCRIPT_ROOT = ""; </script> <script src="/static/scripts.js?v=20240926"> </script> <script src="https://static.zbmath.org/contrib/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script> <script type="text/x-mathjax-config"> MathJax.Hub.Config({ "HTML-CSS": { preferredFont: "TeX", availableFonts: [ "STIX", "TeX" ], linebreaks: { automatic: true }, EqnChunk: (MathJax.Hub.Browser.isMobile ? 10 : 50) }, tex2jax: { processEscapes: true, ignoreClass: "tex2jax_ignore|dno" }, TeX: { Macros: { Aut: "\\operatorname{Aut}", Hom: "\\operatorname{Hom}" }, noUndefined: { attributes: { mathcolor: "#039", //"red", mathbackground: "white", //"#FFEEEE", mathsize: "90%" } } }, messageStyle: "none" }); </script> <script type="text/javascript"> $(document).ready(function() { $("#MathInput").stop(true, true).keyup(function() { $.ajax({ url: "/mwsq/", type: "POST", data: { query : $("#MathInput").val() }, dataType: "text" }) .done(function(xml) { $("#MathPreview").html(xml); $(window).resize(); }); }); var press = jQuery.Event("keyup"); press.ctrlKey = false; press.which = 40; $("#MathInput").trigger(press); }); </script> <div id="new_tab_icon" style="display: none"> <span class="glyphicon glyphicon-new-window" aria-hidden="true"></span><span class="sr-only">(opens in new tab)</span></div> </body> </html>

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