Exterior degree of infinite groups

TL;DR

This paper extends the concept of exterior degree from finite to infinite groups, establishing inequalities and structural restrictions that generalize previous finite group results.

Contribution

It introduces the exterior degree for infinite groups and derives new inequalities that provide insights into their structure.

Findings

Established inequalities for the exterior degree of infinite groups.

Generalized finite group results to the infinite case.

Provided structural restrictions based on exterior degree.

Abstract

The exterior degree of a finite group has been introduced in [P. Niroomand and R. Rezaei, On the exterior degree of finite groups, Comm. Algebra 39 (2011), 335--343] and the present paper is devoted to study the exterior degree of infinite groups. We find some inequalities of combinatorial nature, which generalize those of the finite case and allow us to get structural restrictions for the whole group.