Almost central involutions in split extensions of Coxeter groups by graph automorphisms

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3 Citations (Scopus)

Abstract

Given a split extension W ⋊ G, where W is an arbitrary Coxeter group and G a group of automorphisms of the Coxeter graph of W, we determine all involutions in W ⋊ G whose centralizers are of finite index. Our result has applications to many problems such as the isomorphism problem for general Coxeter groups. In the course of the proof, some properties of certain special elements and of fixed-point subgroups of graph automorphisms in Coxeter groups which are of independent interest are given.

Original languageEnglish
Pages (from-to)139-166
Number of pages28
JournalJournal of Group Theory
Volume10
Issue number2
DOIs
Publication statusPublished - Mar 20 2007
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

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