Conjugately biprimitively finite groups with the primary minimal condition
type: Item
instance of: scholarly article
title: Conjugately biprimitively finite groups with the primary minimal condition
zbMATH Open document ID: 0568.20038
DOI: 10.1007/BF01978669
published in: Algebra and Logic
publication date: 1983-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/187218
review text: The author continues the study of conjugately biprimitively finite groups which were introduced by Shunkov. By definition a group G is conjugately biprimitively finite if for any finite subgroup H of G each pair of elements of equal prime order from \(N_ G(H)/H\) generates a finite subgroup of \(N_ G(H)/H\). It is proved that if a group satisfying the condition of the title is periodic then it is locally finite. It is also proved that if a group satisfying the condition of the title has only finite Sylow p-subgroups then it has a unique maximal periodic subgroup.
Mathematics Subject Classification ID: 20F50
Mathematics Subject Classification ID: 20E25
Mathematics Subject Classification ID: 20E07
Mathematics Subject Classification ID: 20E15
zbMATH DE Number: 3906736
zbMATH Keywords: locally finite groups
zbMATH Keywords: conjugately biprimitively finite groups
zbMATH Keywords: finite Sylow p-subgroups
zbMATH Keywords: maximal periodic subgroup
author: A. K. Shlepkin
MaRDI profile type: Publication
cites work: Q4149613
cites work: On locally finite groups with the condition of primary minimality for subgroups
cites work: Q5776638
cites work: Q4118011
cites work: Q3667072
cites work: Q3964761
cites work: Infinite groups saturated by Frobenius subgroups
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description: scientific article; zbMATH DE number 3906736