On the question of existence of minimal non-FC-groups
type: Item
instance of: scholarly article
title: On the question of existence of minimal non-FC-groups
zbMATH Open document ID: 0941.20040
DOI: 10.1007/BF02674120
author: V. V. Belyaev
published in: Siberian Mathematical Journal
publication date: 2000-04-16T00:00:00Z
review text: The main result of the article states that a perfect locally finite non-FC-group all whose subgroups are FC-groups has a nontrivial finitary permutation representation. This is a generalization of a result by \textit{F. Leinen} and \textit{O. Puglisi} [J. Lond. Math. Soc., II. Ser. 48, No. 1, 59-76 (1993; Zbl 0792.20051)] asserting that such a group has a nontrivial finitary linear representation.
Mathematics Subject Classification ID: 20F24
Mathematics Subject Classification ID: 20F50
zbMATH DE Number: 1432318
zbMATH Keywords: finitary permutation representations
zbMATH Keywords: perfect locally finite groups
zbMATH Keywords: minimal non-FC-groups
reviewed by: Vl. D. Mazurov
MaRDI profile type: Publication
cites work: Locally finite minimal non-FC-groups
cites work: Locally graded minimal non \(CC\)-groups are \(p\)-groups
cites work: Unipotent Finitary Linear Groups
cites work: Q4175427
description: scientific article; zbMATH DE number 1432318