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Commuting powers and exterior degree of finite groups
Peyman Niroomand,Rashid Rezaei,Francesco G. Russo 대한수학회 2012 대한수학회지 Vol.49 No.4
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.
COMMUTING POWERS AND EXTERIOR DEGREE OF FINITE GROUPS
Niroomand, Peyman,Rezaei, Rashid,Russo, Francesco G. Korean Mathematical Society 2012 대한수학회지 Vol.49 No.4
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 $x{\wedge}y=1_{G{\wedge}G}$ in the exterior square $G{\wedge}G$ 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 $h^m{\wedge}k$ of $H{\wedge}K$ such that $h^m{\wedge}k=1_{H{\wedge}K}$, where $m{\geq}1$ and $H$ and $K$ are arbitrary subgroups of $G$.