On generalized commutativity degree of a finite group.
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.
scientific article; zbMATH DE number 5996736
scientific article