Free subgroups of branch groups.
type: Item
instance of: scholarly article
title: Free subgroups of branch groups.
zbMATH Open document ID: 1044.20012
author: D. Massart
published in: Archiv der Mathematik
publication date: 2003-10-16T00:00:00Z
review text: The main aim of the paper is to construct finitely generated branch groups on the binary tree which contain non-cyclic free subgroups. This answers three of four points of Problem 15.14 in the Kourovka Notebook. Namely: Do there exist finitely generated branch groups (a) that are non-amenable; (c) that contain the free group \(F_2\); (d) that have exponential growth? The answer to point (c) is given by Theorem 1. There exist finitely generated branch groups defined on the binary tree containing non-cyclic free subgroups. -- Further, the groups with non-cyclic free subgroup have exponential growth, and are non-amenable. These answer points (a) and (d).
reviewed by: Vahagn H. Mikaelian
Mathematics Subject Classification ID: 20E08
Mathematics Subject Classification ID: 20E22
Mathematics Subject Classification ID: 20E07
zbMATH DE Number: 1993477
zbMATH Keywords: groups acting on trees
zbMATH Keywords: branch groups
zbMATH Keywords: free subgroups
MaRDI profile type: Publication
full work available at URL: s00013-003-0812-2
OpenAlex ID: W2033309209
DOI: 10.1007/S00013-003-0812-2
description: scientific article; zbMATH DE number 1993477