Subgroup S-commutativity degrees of finite groups.
type: Item
instance of: scholarly article
title: Subgroup S-commutativity degrees of finite groups.
zbMATH Open document ID: 1252.20025
author: Daniele Ettore Otera
author: Francesco Russo
published in: Bulletin of the Belgian Mathematical Society - Simon Stevin
publication date: 2012-06-28T00:00:00Z
full work available at URL: https://arxiv.org/abs/1009.2171
full work available at URL: https://projecteuclid.org/euclid.bbms/1337864280
review text: In this paper a generalization of the subgroup commutativity degree of a finite group \(G\) is given. More precisely, the authors define and study the subgroup \(S\)-commutativity degree of \(G\), i.e. the number of permuting subgroups \((H,K)\in sn(G)\times M(G)\) (where \(sn(G)\) is the lattice of subnormal subgroups of \(G\) and \(M(G)\) denotes the set of maximal subgroups of \(G\)), divided by \(|sn(G)||M(G)|\). This new quantity measures the probability that subnormal subgroups commute with maximal subgroups.
reviewed by: Marius Tărnăuceanu
Mathematics Subject Classification ID: 20D60
Mathematics Subject Classification ID: 20D30
Mathematics Subject Classification ID: 20D40
Mathematics Subject Classification ID: 20D35
Mathematics Subject Classification ID: 20P05
zbMATH DE Number: 6050946
zbMATH Keywords: subgroup commutativity degrees
zbMATH Keywords: Möbius numbers
zbMATH Keywords: finite groups
zbMATH Keywords: numbers of permuting subgroups
zbMATH Keywords: subgroup lattices
zbMATH Keywords: lattices of subnormal subgroups
zbMATH Keywords: maximal subgroups
MaRDI profile type: Publication
arXiv ID: 1009.2171
description: scientific article; zbMATH DE number 6050946