On the multiple exterior degree of finite groups

TL;DR

This paper introduces the multiple exterior degree as a new group invariant for finite groups, exploring its relationships with the Schur multiplier, capability, and other group properties.

Contribution

It generalizes the exterior degree concept to multiple exterior degrees and investigates their connections with multiple commutativity degree and group capability.

Findings

Established relations between multiple exterior degree and Schur multiplier.

Connected multiple exterior degree with multiple commutativity degree.

Provided criteria linking multiple exterior degree to group capability.

Abstract

Recently, two first authors have introduced a group invariant, which is related to the number of elements $x$ and $y$ of a finite group $G$ such that $x\wedge y=1$ in the exterior square $G\wedge G$ of $G$. Research on this probability gives some relations between the concept and Schur multiplier and the capability of finite groups. In the present paper, we will generalize the concept of exterior degree of groups and we will introduce the multiple exterior degree of finite groups. Among the other results, we will state some results between the multiple exterior degree, multiple commutativity degree and capability of finite groups.