The third commutant membership problem in solvable groups
type: Item
instance of: scholarly article
title: The third commutant membership problem in solvable groups
zbMATH Open document ID: 0917.20029
DOI: 10.1007/BF02673904
author: I. V. Latkin
published in: Siberian Mathematical Journal
publication date: 1999-05-11T00:00:00Z
review text: It is known that, for every finitely generated and recursively defined group, the second commutant membership problem is solvable [see \textit{I. V. Latkin}, Sib. Mat. Zh. 28, No. 5(165), 102-110 (1987; Zbl 0654.03027)]. In the article under review, the following theorem is proven: There is a finitely presented solvable group of derived length 4 for which the word problem is solvable and the third commutant membership problem is unsolvable.
Mathematics Subject Classification ID: 20F10
Mathematics Subject Classification ID: 03D40
Mathematics Subject Classification ID: 03D45
Mathematics Subject Classification ID: 20F14
Mathematics Subject Classification ID: 20F16
zbMATH DE Number: 1286293
zbMATH Keywords: finitely presented solvable groups
zbMATH Keywords: occurrence problem
zbMATH Keywords: Minsky machine
zbMATH Keywords: solvable word problem
MaRDI profile type: Publication
cites work: Q3944763
cites work: Algorithmically insoluble problems about finitely presented solvable groups, Lie and associative algebras. I
cites work: Algorithmically insoluble problems about finitely presented solvable groups, Lie and associative algebras. II
cites work: Q3778735
cites work: Q4047720
full work available at URL: https://doi.org/10.1007/bf02673904
OpenAlex ID: W2071799976
description: scientific article; zbMATH DE number 1286293