The Higman--Thompson groups \(V_n\) are \((2,2,2)\)-generated

We provide a family of generating sets \(S_{\alpha}\) of the Higman--Thompson groups \(V_n\) that are parametrized by certain sequences \(\alpha\) of elements in \(V_n\). These generating sets consist of \(3\) involutions \(\sigma\), \(\tau\), and \(s_{\alpha}\), where the latter involution is inspi...

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Bibliographic Details
Published in:arXiv.org 2024-11
Main Authors: Schesler, Eduard, Skipper, Rachel, Wu, Xiaolei
Format: Article
Language:English
Online Access:Get full text
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Summary:We provide a family of generating sets \(S_{\alpha}\) of the Higman--Thompson groups \(V_n\) that are parametrized by certain sequences \(\alpha\) of elements in \(V_n\). These generating sets consist of \(3\) involutions \(\sigma\), \(\tau\), and \(s_{\alpha}\), where the latter involution is inspired by the class of spinal elements in the theory of branch groups. In particular this shows the existence of generating sets of \(V_n\) that consist of \(3\) involutions.
ISSN:2331-8422