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 $G$.