On the commutativity degree of compact groups
type: Item
instance of: scholarly article
title: On the commutativity degree of compact groups
zbMATH Open document ID: 1186.22009
author: Rashid Rezaei
author: A. Erfanian
published in: Archiv der Mathematik
publication date: 2009-11-25T00:00:00Z
review text: In any finite group \(G\), for every \(n\geq 2\) the \(n\)-th commutative degree \(d_n(G)\) is the probability that a randomly chosen ordered \((n+1)\)-tuple of the group elements is mutually commuting. The aim of this paper is to generalize this definition to every compact group, which is possible since such a group can be considered as a probability space with respect to the normalized Haar measure. It is proved that if \(G\) and \(H\) are two isoclinic compact groups, then \(d_n(G)=d_n(H)\). Moreover \(d_n(G)\leq (3\cdot 2^n-1)/2^{2n+1}\) for every nonabelian compact group \(G\).
reviewed by: Andrea Lucchini
Mathematics Subject Classification ID: 22C05
Mathematics Subject Classification ID: 20D60
Mathematics Subject Classification ID: 20P05
Mathematics Subject Classification ID: 20D08
zbMATH DE Number: 5638430
zbMATH Keywords: commutativity degree
zbMATH Keywords: \(n\)th commutativity degree
zbMATH Keywords: compact groups
zbMATH Keywords: isoclinism
MaRDI profile type: Publication
full work available at URL: s00013-009-0041-4
OpenAlex ID: W2010873418
cites work: On the Relative Commutativity Degree of a Subgroup of a Finite Group
cites work: The number of conjugacy classes in a finite group
cites work: On the commuting probability in finite groups.
cites work: What is the Probability that Two Group Elements Commute?
cites work: The structure of compact groups. A primer for the student -- a handbook for the expert
cites work: Isoclinism classes and commutativity degrees of finite groups
cites work: Relative Number of Non-Invariant Operators in a Group
cites work: Q5550080
cites work: Q5654235
cites work: Multiplicators and groups with finite central factor-groups
DOI: 10.1007/S00013-009-0041-4
description: scientific article; zbMATH DE number 5638430