Exterior degree of infinite groups
Rashid Rezaei (Malayer University, Malayer, Iran), Francesco G., Russo (Universita' degli Studi di Palermo, Palermo, Italy)

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.
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Taxonomy
TopicsFinite Group Theory Research · Rings, Modules, and Algebras · Limits and Structures in Graph Theory
