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  $G$.

Keywords

• automorphism group,autocommutativity degree,autoisoclinism

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