Groups with finiteness conditions and other restrictions
type: Item
instance of: scholarly article
title: Groups with finiteness conditions and other restrictions
zbMATH Open document ID: 0675.20021
DOI: 10.1007/BF01061298
author: V. S. Charin
author: D. I. Zajtsev
published in: Ukrainian Mathematical Journal
publication date: 1988-01-01T00:00:00Z
review text: This is a survey article concerning the groups mentioned in the title. In particular it emphasizes the role of S. N. Chernikov who began a systematic study of these groups in the 1930's. In his honour an almost abelian group with minimum condition for subgroups is called a Chernikov group. The various sections are: 1. Minimality condition for subgroups, 2. Local properties of groups, 3. Complete groups, 4. Minimality condition for various forms of subgroups, 5. Layer-finite groups and their generalizations, 6. Restrictions for infinite subgroups, 7. Groups with complemented subgroups.
Mathematics Subject Classification ID: 20E15
Mathematics Subject Classification ID: 20E34
Mathematics Subject Classification ID: 20F22
Mathematics Subject Classification ID: 20E07
zbMATH DE Number: 4105213
zbMATH Keywords: finiteness conditions
zbMATH Keywords: generalized soluble groups
zbMATH Keywords: minimality conditions
zbMATH Keywords: complete groups
zbMATH Keywords: layer-finite groups
zbMATH Keywords: survey
zbMATH Keywords: minimum condition for subgroups
zbMATH Keywords: Chernikov group
zbMATH Keywords: complemented subgroups
reviewed by: Bernhard Amberg
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4105213