Commuting powers and exterior degree of finite groups

Abstract

Recently, we have introduced a group invariant, which is related to the number of elements x and y of a finite group G such that x ∧ y = 1 G∧G in the exterior square G ∧ G of G. This number gives restrictions on the Schur multiplier of G and, consequently, large classes of groups can be described. In the present paper we generalize the previous investigations on the topic, focusing on the number of elements of the form h m ∧ k of H ∧ K such that h m ∧ k = 1 H∧K, where m ≥ 1 and H and K are arbitrary subgroups of G. ©2012 The Korean Mathematical Society.