Occurrence problem for free solvable groups
type: Item
instance of: scholarly article
title: Occurrence problem for free solvable groups
zbMATH Open document ID: 0854.20044
DOI: 10.1007/BF00750164
published in: Algebra and Logic
publication date: 1996-03-27T00:00:00Z
full work available at URL: https://eudml.org/doc/187721
review text: The author studies the problem of the existence of an algorithm verifying whether systems of linear equations over a group ring of a free metabelian group are solvable. He proves that if \(G\) is a free metabelian group (of large enough rank), then the occurrence problem for right ideals of the ring \(ZG\) is undecidable. Also he shows that the occurrence problem for free solvable groups of derived length \(\geq 3\) is undecidable. It is given an example of a group with undecidable word problem which is finitely presented in the variety of solvable groups of derived length \(\geq 3\) and whose defining relations are taken from the last commutant.
Mathematics Subject Classification ID: 20F10
Mathematics Subject Classification ID: 20F16
Mathematics Subject Classification ID: 20C07
Mathematics Subject Classification ID: 16S34
zbMATH DE Number: 848951
zbMATH Keywords: systems of linear equations
zbMATH Keywords: group rings
zbMATH Keywords: free metabelian groups
zbMATH Keywords: occurrence problem
zbMATH Keywords: right ideals
zbMATH Keywords: free solvable groups
zbMATH Keywords: undecidable word problem
zbMATH Keywords: variety of solvable groups
author: Ualbai Umirbaev
reviewed by: Alexander Ivanovich Budkin
MaRDI profile type: Publication
cites work: Groups of cohomological dimension one
cites work: Free lattice-ordered groups
cites work: Q3944763
cites work: The occurrence problem for Lie algebras
cites work: Free differential calculus. I: Derivation in the free group ring. II: The isomerphism problem of groups. III: Subgroups
cites work: Automorphisms of Free Metabelian Groups
OpenAlex ID: W1982922907
description: scientific article; zbMATH DE number 848951