# COMMUTING POWERS AND EXTERIOR DEGREE OF FINITE GROUPS

• Niroomand, Peyman ;
• Rezaei, Rashid ;
• Russo, Francesco G.
• Published : 2012.07.01
• 49 6

#### 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 $x{\wedge}y=1_{G{\wedge}G}$ 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 $G$.

#### Keywords

m-th relative exterior degree;commutativity degree;exterior product;Schur multiplier;homological algebra

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