On tame automorphisms of some metabelian groups
type: Item
instance of: scholarly article
title: On tame automorphisms of some metabelian groups
zbMATH Open document ID: 0956.20016
DOI: 10.1007/BF02674607
author: Evgenii I. Timoshenko
published in: Siberian Mathematical Journal
publication date: 2000-11-21T00:00:00Z
full work available at URL: https://eudml.org/doc/120819
review text: Let \(M\) be a variety of groups and let \(F_r(M)\) be the free group of rank \(r\) of this variety. Recall that an automorphism \(\alpha\) of \(F_r(M)\) is tame if there exists an automorphism \(\overline\alpha\) of the free group \(F_r\) of rank \(r\) such that \(\alpha\) is induced by \(\overline\alpha\). Otherwise \(\alpha\) is said to be wild. The author finds necessary and sufficient conditions for an automorphism \(\alpha\) to be tame in the case when \(M\) is a variety of metabelian groups of nilpotency class \(m\) (\(m\geq 3\)). The author also proves that the following problem has an algorithmic solution: Is an automorphism \(\alpha\) of \(F_r(M)\) tame?
Mathematics Subject Classification ID: 20E10
Mathematics Subject Classification ID: 20F16
Mathematics Subject Classification ID: 20F10
Mathematics Subject Classification ID: 20E36
Mathematics Subject Classification ID: 20E05
zbMATH DE Number: 1534390
zbMATH Keywords: tame automorphisms
zbMATH Keywords: metabelian groups of bounded nilpotency class
zbMATH Keywords: varieties of metabelian groups
zbMATH Keywords: recognition algorithms for tame automorphisms
zbMATH Keywords: wild automorphisms
zbMATH Keywords: relatively free groups
MaRDI profile type: Publication
cites work: Triples of 2 × 2 Matrices Which Generate Free Groups
cites work: IA automorphisms of free and free metabelian groups
cites work: Aut(F) →Aut(F/F � � ) is Surjective for Free Group F of Rank 4
cites work: Primitivity in Free Groups and Free Metabelian Groups
cites work: Q4866223
cites work: Tame automorphisms of finitely generated abelian groups
cites work: Finite separability of tameness and primmvity in certain relatively free groups
cites work: Q4726454
cites work: Primitivity in the free groups of the variety UmUn
cites work: Q3953969
OpenAlex ID: W2056609148
description: scientific article; zbMATH DE number 1534390