On centralizers of elements of groups acting on trees with inversions.
type: Item
instance of: scholarly article
title: On centralizers of elements of groups acting on trees with inversions.
zbMATH Open document ID: 1063.20029
DOI: 10.1155/S0161171203205305
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2003-06-18T00:00:00Z
full work available at URL: https://eudml.org/doc/51301
review text: Summary: A subgroup \(H\) of a group \(G\) is called malnormal in \(G\) if it satisfies the condition that if \(g\in G\) and \(h\in H\), \(h\neq 1\), such that \(ghg^{-1}\in H\), then \(g\in H\). We show that if \(G\) is a group acting on a tree \(X\) with inversions such that each edge stabilizer is malnormal in \(G\), then the centralizer \(C(g)\) of each nontrivial element \(g\) of \(G\) is in a vertex stabilizer if \(g\) is in that vertex stabilizer. If \(g\) is not in any vertex stabilizer, then \(C(g)\) is infinite cyclic if \(g\) does not transfer an edge of \(X\) to its inverse. Otherwise, \(C(g)\) is finite cyclic of order 2.
Mathematics Subject Classification ID: 20E08
Mathematics Subject Classification ID: 20E07
Mathematics Subject Classification ID: 20E06
Mathematics Subject Classification ID: 20F65
zbMATH DE Number: 1930026
zbMATH Keywords: malnormal subgroups
zbMATH Keywords: groups acting on trees
zbMATH Keywords: edge stabilizers
zbMATH Keywords: centralizers
zbMATH Keywords: vertex stabilizers
author: R. M. S. Mahmood
MaRDI profile type: Publication
OpenAlex ID: W2106266498
description: scientific article; zbMATH DE number 1930026