On generalized autocommutativity degree of finite groups

Authors : Parama DUTTA, Rajat KANTİ NATH

Pages : 472-478

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Publication Date : 2019-04-01

Article Type : Research Paper

Abstract :Let $H$  be  a subgroup of a finite group $G$ and Aut$insert ignore into journalissuearticles values(G);$ 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$insert ignore into journalissuearticles values(G);$ , is equal to a given element of  $G$.
Keywords : automorphism group, autocommutativity degree, autoisoclinism