On Baer's problem and properties of \(M''\)-groups
type: Item
instance of: scholarly article
title: On Baer's problem and properties of \(M''\)-groups
zbMATH Open document ID: 1031.20020
author: N. S. Chernikov
published in: Illinois Journal of Mathematics
publication date: 2003-10-16T00:00:00Z
review text: In 1949, R. Baer raised the following question: If the group \(G\) is socle and for each \(\alpha<\gamma\) \(\text{Soc}_{\alpha+1}(G)/\text{Soc}_\alpha(G)\) is a direct product of finitely many minimal normal subgroups of\break \(G/\text{Soc}_\alpha(G)\), does it follow that \(G\) satisfies the minimal condition for normal subgroup? Later, in 1959, S. N. Chernikov motivated by this question raised his two problems regarding \(M''\)- and \(M'\)-groups. These questions have been answered in the negative by Ju. M. Mezebovskij (1972) and N. S. Chernikov (1991) independently. The article under review establishes new properties of \(M''\)-groups and contains new counterexamples to the problems of R. Baer and S. N. Chernikov.
Mathematics Subject Classification ID: 20E15
Mathematics Subject Classification ID: 20F22
Mathematics Subject Classification ID: 20F24
Mathematics Subject Classification ID: 20F50
Mathematics Subject Classification ID: 20E07
zbMATH DE Number: 1993619
zbMATH Keywords: \(M''\)-groups
zbMATH Keywords: \(M'\)-groups
zbMATH Keywords: socle groups
zbMATH Keywords: periodic FC-groups
zbMATH Keywords: products of normal semisimple subgroups
zbMATH Keywords: minimal normal subgroups
zbMATH Keywords: minimal condition on normal subgroups
reviewed by: Igor Subbotin
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1993619