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arXiv · 1102.2304

Commuting powers and exterior degree of finite groups

Peyman Niroomand·Rashid Rezaei·Francesco G. Russo
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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 $x \wedge y = 1_{G \wedge G}$ 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 $m \ge 1$ and $H$ and $K$ are arbitrary subgroups of $G$.

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Peyman Niroomand, Rashid Rezaei, Francesco G. Russo. 2011-02-11. Commuting powers and exterior degree of finite groups. https://doi.org/10.4134/jkms.2012.49.4.855

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