Algorithmically insoluble problems about finitely presented solvable groups, Lie and associative algebras. II
type: Item
instance of: scholarly article
title: Algorithmically insoluble problems about finitely presented solvable groups, Lie and associative algebras. II
zbMATH Open document ID: 0579.20031
DOI: 10.1016/0021-8693(85)90085-7
author: Gilbert Baumslag
author: Dion Gildenhuys
author: Ralph Strebel
published in: Journal of Algebra
publication date: 1985-01-01T00:00:00Z
review text: This is the second paper in a series devoted to algorithmic problems [for the first one see J. Pure Appl. Algebra 39, 53-94 (1986; Zbl 0577.20021)]. Here the authors use a variation of O. Kharlampovich's example of a finitely presented group of derived length 3 with insoluble word problem to derive some further results on algorithmic undecidability in soluble groups. They produce a recursive class of finitely presented groups of soluble length 3 with insoluble isomorphism problem. A recursive class of finitely presented groups of soluble length 3 or 4 is exhibited with no algorithm for determining the exact length of any of these groups. They also construct a class of soluble groups of derived length 3 where the problem of direct decomposability is insoluble. Finally they give an example of a finitely presented soluble group of derived length 3 where many properties of elements are insoluble.
Mathematics Subject Classification ID: 20F10
Mathematics Subject Classification ID: 20F16
Mathematics Subject Classification ID: 20F05
zbMATH DE Number: 3927200
zbMATH Keywords: algorithmic problems
zbMATH Keywords: finitely presented group
zbMATH Keywords: insoluble word problem
zbMATH Keywords: algorithmic undecidability in soluble groups
zbMATH Keywords: isomorphism problem
zbMATH Keywords: direct decomposability
Wikidata QID: Q115366933
MaRDI profile type: Publication
full work available at URL: 0021-8693(85)90085-7
OpenAlex ID: W4205201762
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description: scientific article; zbMATH DE number 3927200