On generalized commutativity degree of a finite group.
type: Item
instance of: scholarly article
title: On generalized commutativity degree of a finite group.
zbMATH Open document ID: 1237.20063
DOI: 10.1216/RMJ-2011-41-6-1987
published in: Rocky Mountain Journal of Mathematics
publication date: 2012-01-12T00:00:00Z
review text: Let \(G\) be a finite group. The generalized commutator of an \(n\)-tuple \((x_1,x_2,\dots,x_n)\in G^n\) is defined as the product \(x_1x_2\cdots x_nx_1^{-1}x_2^{-1}\cdots x_n^{-1}\). The object of this paper is to study the probability that the generalized commutator of an arbitrarily chosen \(n\)-tuple of group elements equals a given group element \(g\). In the particular case when \(n=2\) and \(g=1\) one gets the commutativity degree of \(G\), i.e., the probability that two arbitrarily chosen elements of \(G\) commute.
reviewed by: Andrea Lucchini
Mathematics Subject Classification ID: 20P05
Mathematics Subject Classification ID: 20D60
Mathematics Subject Classification ID: 20C15
zbMATH DE Number: 5996736
zbMATH Keywords: finite groups
zbMATH Keywords: group characters
zbMATH Keywords: commutativity degrees
zbMATH Keywords: conjugacy class sizes
zbMATH Keywords: generalized commutators
author: Rajat Kanti Nath
author: A. K. Das
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 5996736