In this paper we introduce and study the concept of subgroup commutativity degree of a finite group G. This quantity measures the probability of two random subgroups of G commuting. Explicit formulas are obtained for some particular classes of finite groups.

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In this paper a new equivalence relation for classifying the fuzzy subgroups of finite groups is introduced and studied. This generalizes the equivalence relation defined on the lattice of fuzzy subgroups of a finite group that has been used in our previous papers. Explicit formulas for the number of distinct fuzzy subgroups with respect to the new equivalence relation are obtained in some particular cases.

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In this note we give a generalization of the well-known Menon's identity. This is based on applying the Burnside's lemma to a certain group action.