Conditions of finiteness in Aleshin-type groups
type: Item
instance of: scholarly article
title: Conditions of finiteness in Aleshin-type groups
zbMATH Open document ID: 0799.20035
DOI: 10.1007/BF01978559
author: A. V. Rozhkov
published in: Algebra and Logic
publication date: 1992-09-27T00:00:00Z
review text: The author continues his investigation of so called Aleshin-type groups - - infinite finitely generated periodic groups which can be constructed for some sequence of primes. A group \(G\) is said to be infinitely prime, iff the index of every nontrivial normal subgroup \(N\) is \(G\) is finite. A criterion of infinite primeness is presented in the case of odd primes in the sequences. It is proved that every binary finite such group is locally finite.
Mathematics Subject Classification ID: 20F50
Mathematics Subject Classification ID: 20F14
Mathematics Subject Classification ID: 20F05
Mathematics Subject Classification ID: 20E07
Mathematics Subject Classification ID: 20E25
zbMATH DE Number: 59394
zbMATH Keywords: central series
zbMATH Keywords: binary finite group
zbMATH Keywords: infinitely prime group
zbMATH Keywords: Aleshin-type groups
zbMATH Keywords: infinite finitely generated periodic groups
zbMATH Keywords: infinite primeness
reviewed by: Vitaliĭ Roman'kov
MaRDI profile type: Publication
cites work: Q4722255
cites work: Q4745979
cites work: Some infinite \(p\)-groups
cites work: Q3734667
cites work: Q3794400
cites work: Subgroups of certain groups of Aleshin type
description: scientific article; zbMATH DE number 59394