Universal theories for free solvable groups.
type: Item
instance of: scholarly article
title: Universal theories for free solvable groups.
zbMATH Open document ID: 1267.20052
author: Nikolai S. Romanovskiy
published in: Algebra and Logic
publication date: 2013-01-03T00:00:00Z
review text: A group \(G\) has a decidable universal theory if there is an algorithm which decides whether or not a universal sentence is true in \(G\). \textit{O. Chapuis} proved [in J. Algebra 176, No. 2, 368-391 (1995; Zbl 0860.20024)] that free metabelian groups, as well as groups close to these, have decidable universal theories. It is proved in the paper under review that a free solvable group of rank \(\geq 2\) of derived length at least 4 has undecidable universal theory. A similar question about a free solvable group of derived length 3 is still open.
Mathematics Subject Classification ID: 20F10
Mathematics Subject Classification ID: 20F16
Mathematics Subject Classification ID: 03C60
Mathematics Subject Classification ID: 20A15
zbMATH DE Number: 6121538
zbMATH Keywords: universal theories
zbMATH Keywords: decidable theories
zbMATH Keywords: free solvable groups
reviewed by: Vitaliĭ Roman'kov
MaRDI profile type: Publication
full work available at URL: s10469-012-9188-3
OpenAlex ID: W2048068031
cites work: Universal theory of certain solvable groups and bounded Ore group rings
cites work: ∀-free metabelian groups
cites work: Q4819916
cites work: On the theories of free solvable groups
cites work: Q4951274
DOI: 10.1007/S10469-012-9188-3
description: scientific article; zbMATH DE number 6121538