Finite automata of polynomial growth do not generate a free group.
type: Item
instance of: scholarly article
title: Finite automata of polynomial growth do not generate a free group.
zbMATH Open document ID: 1075.20011
author: Xianqiang Yang
published in: Geometriae Dedicata
publication date: 2005-03-15T00:00:00Z
review text: In an earlier paper, the author conjectured that finite-state automata of polynomial growth cannot generate free groups of rank 2. In this paper, the author proves, under some natural hypotheses, that finite-state automorphisms of polynomial growth cannot generate free subgroups of rank 2 of the group of automorphisms of a regular rooted tree of arbitrary degree.
reviewed by: F. Blanchet-Sadri
Mathematics Subject Classification ID: 20E08
Mathematics Subject Classification ID: 20F05
Mathematics Subject Classification ID: 20F10
Mathematics Subject Classification ID: 68Q45
zbMATH DE Number: 2145817
zbMATH Keywords: regular rooted trees
zbMATH Keywords: automorphisms of trees
zbMATH Keywords: finite automata
zbMATH Keywords: polynomial growth
zbMATH Keywords: free groups
MaRDI profile type: Publication
full work available at URL: s10711-004-2368-0
OpenAlex ID: W2083227394
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DOI: 10.1007/S10711-004-2368-0
description: scientific article; zbMATH DE number 2145817