On generalized autocommutativity degree of finite groups

Abstract

Let H be a subgroup of a finite group G and Aut(G) be the automorphism group of G. In this paper we introduce and study the probability that the autocommutator of a randomly chosen pair of elements, one from H and the other from Aut(G), is equal to a given element of G. Mathematics Subject Classification (2010). 20D60, 20P05, 20F28