Commuting powers and exterior degree of finite groups
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Recently, we have introduced a group invariant, which is re-lated to the number of elements x and y of a nite group G such that x ^ y = 1G^G in the exterior square G ^ G of G. This number gives re-strictions 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 K are arbitrary subgroups of G.
Abstract
Recently, we have introduced a group invariant, which is re-lated to the number of elements x and y of a nite group G such that x ^ y = 1G^G in the exterior square G ^ G of G. This number gives re-strictions 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 K are arbitrary subgroups of G.
참고문헌 (12)
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