Commuting powers and exterior degree of finite groups

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 $G$.

to appear in the J. Korean Math. Soc. with revisions

References in corpus (2)

• Relative n-isoclinism classes and relative n-th nilpotency degree of finite groups
• The exterior degree of a pair of finite groups

Cited by in corpus (2)

• Remarks on the tensor degree of finite groups
• Considerations on the subgroup commutativity degree and related notions