Theory of groups that act on trees
type: Item
instance of: scholarly article
title: Theory of groups that act on trees
zbMATH Open document ID: 0571.20017
DOI: 10.1007/BF01978668
author: V. A. Churkin
published in: Algebra and Logic
publication date: 1983-01-01T00:00:00Z
review text: The author gives a combinatorial proof of the well known theorem of Bass and \textit{J.-P. Serre} [Arbres, amalgams, \(SL_ 2\), Astérisque 46 (1977; Zbl 0369.20013)] on the structure of groups acting on trees. His proof is based on a theorem of \textit{A. M. Macbeath} [Ann. Math., II. Ser. 79, 473-488 (1964; Zbl 0122.175)] which gives a presentation for a group acting on a topological space in terms of translates of a fundamental region. A proof of Macbeath's theorem in the special case needed is included. The English translation contains a few mistakes, e.g. it should read ''Tietze transformations'' instead of ''Tits transf.''.
reviewed by: Frank Herrlich
Mathematics Subject Classification ID: 20E06
Mathematics Subject Classification ID: 20F05
Mathematics Subject Classification ID: 05C25
zbMATH DE Number: 3910606
zbMATH Keywords: fundamental group of a graph of groups
zbMATH Keywords: groups acting on trees
zbMATH Keywords: presentation
zbMATH Keywords: fundamental region
MaRDI profile type: Publication
cites work: Groups, trees and projective modules
cites work: Groups of homeomorphisms of a simply connected space
full work available at URL: https://doi.org/10.1007/bf01978668
OpenAlex ID: W1973101493
description: scientific article; zbMATH DE number 3910606