Abstract
In [P. Niroomand, R. Rezaei, On the exterior degree of finite groups, Comm. Algebra 39 (2011), 335-343] it is introduced a group invariant, related to the number of elements x and y of a finite group G, such that x∧y=1G∧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 hm∧k of H∧K such that hm∧k=1H∧K, where m≥1 and H and Kare arbitrary subgroups of G.