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

Document Type : Research Paper


1 Middle Technical University, Technical Instructors Training Institute, Iraq

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


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.


[1] A. Aubad, S. kadem, and A. H. Majeed,The non-zero divisor graph of a ring, IJPAM. 43 (2020) 975–983.
[2] C. Cedillo, R. MacKinney-Romero, M.A. Pizaa, I.A. Robles and R. Villarroel-Flores, Yet Another Graph System,
Yags, Version 0.0.5., 2020.
[3] H. Conway, R. T. Curtis, S. P. Norton and R. A. Parker, Atlas of Finite Groups: Maximal Subgroups and Ordinary
Characters for Simple Groups, Oxford Clarendon Press, 1985.
[4] A. Maksimenko and A. Mamontov, The local finiteness of some groups generated by a conjugacy class of order 3
elements, Siberian Math. J. 3 (2007) 508–518.
[5] S. M. Kasim and A. Nawawi, On diameter of subgraphs of commuting graph in symplectic group for elements of
order three, Sains Malays. 2 (2021) 549–557.
[6] J. Tripp, I. Suleiman, S. Rogers R. Parker, S. Norton, S. Nickerson, S. Linton, J. Bray, A. Wilson and P. Walsh,
A World Wide Web Atlas of Group Representations, 2021.
[7] The GAP Group, GAP Groups, Algorithms, and Programming, Version 4.11.1, 2021.
Volume 12, Issue 2
November 2021
Pages 1855-1860
  • Receive Date: 08 March 2021
  • Revise Date: 27 June 2021
  • Accept Date: 03 July 2021