Autocommuting probability of a finite group relative to its subgroups

الأصل · EN

Let H K be two subgroups of a finite group G and Aut(K) the automorphism group of K. The autocommuting probability of G relative to its subgroups H and K, denoted by Pr(H, Aut(K)), is the probability that the autocommutator of a randomly chosen pair of elements, one from H and the other from Aut(K), is equal to the identity element of G. In this paper, we study Pr(H, Aut(K)) through a generalization.