On inert subgroups of a group.
type: Item
instance of: scholarly article
title: On inert subgroups of a group.
zbMATH Open document ID: 1167.20319
author: Derek J. S. Robinson
published in: Rendiconti del Seminario Matematico della Università di Padova
publication date: 2009-08-13T00:00:00Z
full work available at URL: https://eudml.org/doc/108671
full work available at URL: RSMUP 2006 115 137 0.pdf
review text: Summary: A subgroup \(H\) of a group \(G\) is called inert if \(|H:H\cap H^g|\) is finite for all \(g\) in \(G\). If every subgroup of \(G\) is inert, then \(G\) is said to be inertial. After giving an account of the basic properties of inert subgroups, we study the structure of inertial soluble groups. A classification is obtained for the groups which are finitely generated or have finite Abelian total rank.
Mathematics Subject Classification ID: 20E07
Mathematics Subject Classification ID: 20F16
Mathematics Subject Classification ID: 20F05
zbMATH DE Number: 5595160
zbMATH Keywords: subgroups of finite index
zbMATH Keywords: inert subgroups
zbMATH Keywords: soluble groups
zbMATH Keywords: finitely-generated groups
zbMATH Keywords: groups with finite Abelian total rank
MaRDI profile type: Publication
cites work: Locally finite simple groups as a product of two inert subgroups
cites work: Locally finite groups containing a finite inseparable subgroup
cites work: Totally inert groups
cites work: Soluble products of nilpotent groups
cites work: Q4820338
cites work: Q5488136
cites work: Permutable subgroups of infinite groups
description: scientific article; zbMATH DE number 5595160