Studying the A4-Graphs for elements of order 3 in tits group T and Mathieu group M20

Document Type : Research Paper

Authors

1 Middle Technical University, Technical Instructors Training Institute, Iraq

2 Middle Technical University, Institute of Technology, Baghdad, Iraq

Abstract

Assume that $X$ is a subset of the finite group $G$. The A4-graph is known as a simple graph denoted by $\mathcal{A}_4 (G, X)$ having $X$ as a vertex set and two vertices $x, y \in X,$ is linked by an edges if $x\neq y$ and ${xy}^{-1} = {yx}^{-1}$. In this paper, we consider $\mathcal{A}_4 (G, X)$ when $G$ is either Tits group T or Mathieu group $M_{20}$ and $X$ is $G$-conjugacy class of elements of order three. Valuable results reached, for example, disc structure, girth, clique number, and diameters of the A4-graph.

Keywords