Inert subgroups in infinite simple groups
type: Item
instance of: scholarly article
title: Inert subgroups in infinite simple groups
zbMATH Open document ID: 0831.20033
DOI: 10.1007/BF00975160
author: V. V. Belyaev
published in: Siberian Mathematical Journal
publication date: 1994-11-08T00:00:00Z
review text: Subgroups \(A\) and \(B\) of a group \(G\) are called commensurable if \(A \cap B\) is a subgroup of finite index in \(A\) as well as in \(B\). If a subgroup is commensurable with each of its conjugate subgroups in \(G\) then we call \(A\) inert in \(G\) (the term ``inert subgroup'' was proposed by O. H. Kegel). The present paper is devoted to the study of the relation between the structure of normal subgroups in an inert subgroup and the normal structure of the entire group. We apply the results obtained in this direction to examine the structure of inert subgroups in simple groups.
Mathematics Subject Classification ID: 20E07
Mathematics Subject Classification ID: 20E32
Mathematics Subject Classification ID: 20F50
Mathematics Subject Classification ID: 20F24
Mathematics Subject Classification ID: 20E15
zbMATH DE Number: 652167
zbMATH Keywords: subgroups of finite index
zbMATH Keywords: normal subgroups
zbMATH Keywords: inert subgroups
zbMATH Keywords: simple groups
MaRDI profile type: Publication
cites work: Locally finite groups containing a finite inseparable subgroup
description: scientific article; zbMATH DE number 652167