Quasi-identities of finite nilpotent groups
type: Item
instance of: scholarly article
title: Quasi-identities of finite nilpotent groups
zbMATH Open document ID: 0839.20038
DOI: 10.1007/BF01182099
published in: Algebra Universalis
publication date: 1996-06-10T00:00:00Z
review text: The main theorem of this paper claims the existence of a quasi-identity \(\Phi\) which is true in the free nilpotent class 2 group \(F_2 ({\mathcal N}_2)\) of rank 2, but false in any non-abelian group with no subgroup isomorphic to \(F_2 ({\mathcal N}_2)\), thus giving a negative answer to the question as to whether the quasivariety of torsion-free groups in the quasivariety generated by an infinite set of groups of order the cube of some prime coincides with the quasivariety generated by \(F_2 ({\mathcal N}_2)\). Unfortunately, the reviewer found the proof of one of the main lemmata (Lemma 4) extremely difficult to follow.
reviewed by: Sheila Oates-Williams
Mathematics Subject Classification ID: 20E10
Mathematics Subject Classification ID: 20F18
Mathematics Subject Classification ID: 08C15
Mathematics Subject Classification ID: 20D15
zbMATH DE Number: 836825
zbMATH Keywords: quasi-identities
zbMATH Keywords: free nilpotent class 2 groups
zbMATH Keywords: quasivarieties of torsion-free groups
author: Alexander Ivanovich Budkin
MaRDI profile type: Publication
cites work: Independent axiomatizability of quasivarieties of generalized solvable groups
cites work: Q4745992
description: scientific article; zbMATH DE number 836825