Most Rigid Representation and Cayley Index of Finitely Generated Groups

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This infimum is called the Cayley index of the group. In a recent series of works, we have characterized the infinite finitely generated groups with Cayley index $1$. We complement this characterization by showing that the Cayley index is $2$ in the remaining cases and is attained for a finite generating set. "/> <meta name="DC.Description" xml:lang="en" content=" If $G$ is a group and $S$ a generating set, $G$ canonically embeds into the automorphism group of its Cayley graph and it is natural to try to minimize, over all generating sets, the index of this inclusion. This infimum is called the Cayley index of the group. In a recent series of works, we have characterized the infinite finitely generated groups with Cayley index $1$. We complement this characterization by showing that the Cayley index is $2$ in the remaining cases and is attained for a finite generating set. 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aria-current="page"> Papers </span> </li> </ol> </nav> <article class="obj_article_details"> <h1 class="page_title"> Most Rigid Representation and Cayley Index of Finitely Generated Groups </h1> <div class="row"> <div class="main_entry"> <ul class="item authors"> <li> <span class="name"> Paul-Henry Leemann </span> </li> <li> <span class="name"> Mikael de la Salle </span> </li> </ul> <div class="item doi"> <span class="label"> DOI: </span> <span class="value"> <a href="https://doi.org/10.37236/10512"> https://doi.org/10.37236/10512 </a> </span> </div> <div class="item abstract"> <h3 class="label">Abstract</h3> <p>If $G$ is a group and $S$ a generating set, $G$ canonically embeds into the automorphism group of its Cayley graph and it is natural to try to minimize, over all generating sets, the index of this inclusion. This infimum is called the Cayley index of the group. In a recent series of works, we have characterized the infinite finitely generated groups with Cayley index $1$. We complement this characterization by showing that the Cayley index is $2$ in the remaining cases and is attained for a finite generating set.</p> </div> </div> <div class="entry_details"> <div class="item galleys"> <ul class="value galleys_links"> <li> <a class="obj_galley_link pdf" href="https://www.combinatorics.org/ojs/index.php/eljc/article/view/v29i4p40/pdf"> PDF </a> </li> </ul> </div> <div class="item published"> <div class="label"> Published </div> <div class="value"> 2022-12-16 </div> </div> <div class="item issue"> <div class="sub_item"> <div class="label"> Issue </div> <div class="value"> <a class="title" href="https://www.combinatorics.org/ojs/index.php/eljc/issue/view/Volume29-4"> Volume 29, Issue 4 (2022) </a> </div> </div> <div class="sub_item"> <div class="label"> Article Number </div> <div class="value"> <div class="pages"> P4.40 </div> </div> </div> </div> </div> </div> </article> </div> </div> </div> </div> <script src="https://www.combinatorics.org/ojs/lib/pkp/lib/vendor/components/jquery/jquery.min.js?v=3.1.2.4" type="text/javascript"></script><script src="https://www.combinatorics.org/ojs/lib/pkp/lib/vendor/components/jqueryui/jquery-ui.min.js?v=3.1.2.4" type="text/javascript"></script><script src="https://www.combinatorics.org/ojs/lib/pkp/js/lib/jquery/plugins/jquery.tag-it.js?v=3.1.2.4" type="text/javascript"></script><script src="https://www.combinatorics.org/ojs/plugins/themes/default/js/lib/popper/popper.js?v=3.1.2.4" type="text/javascript"></script><script src="https://www.combinatorics.org/ojs/plugins/themes/default/js/lib/bootstrap/util.js?v=3.1.2.4" type="text/javascript"></script><script src="https://www.combinatorics.org/ojs/plugins/themes/default/js/lib/bootstrap/dropdown.js?v=3.1.2.4" type="text/javascript"></script><script src="https://www.combinatorics.org/ojs/plugins/themes/default/js/main.js?v=3.1.2.4" type="text/javascript"></script><script type="text/javascript"></script> <script type="text/x-mathjax-config"> MathJax.Hub.Config({ tex2jax: {inlineMath: [['$','$'], ['\$','\$']], displayMath: [ ['$$','$$'], ['\\[','\\]'] ], processEnvironments: true, processEscapes: true} }); </script> <script type="text/javascript" async src="https://cdn.jsdelivr.net/npm/mathjax@2.7.9/MathJax.js?config=TeX-MML-AM_CHTML"> </script> </body> </html>

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Most Rigid Representation and Cayley Index of Finitely Generated Groups | The Electronic Journal of Combinatorics