Maximal subset of pairwise non-commuting elements of finite minimal non-Abelian groups

TL;DR

This paper determines the size of the largest set of pairwise non-commuting elements in finite minimal non-abelian groups, providing insights into their algebraic structure.

Contribution

It explicitly calculates the maximal subset size of pairwise non-commuting elements in finite minimal non-abelian groups, a previously unresolved problem.

Findings

Cardinality of maximal non-commuting subsets determined

Results specific to finite minimal non-abelian groups

Enhances understanding of non-abelian group structures

Abstract

Let G be a group. A subset X of G is a set of pairwise non-commuting elements if xy is not equal to yx for any two distinct elements x and y in X. If |X|>=|Y| for any other set of pairwise non-commuting elements Y in G, then X is said to be a maximal subset of pairwise non-commuting elements. In this paper we determine the cardinality of a maximal subset of pairwise non-commuting elements for finite minimal non-abelian groups.