Recognizability of finite groups by Suzuki group

Alireza Khalili Asboei and Seyed Sadegh Salehi Amiri

Address:
A.K. Asboei, Department of Mathematics, Farhangian University, Tehran, Iran
S.S.S. Amiri, Department of Mathematics, Babol Branch, Islamic Azad University, Babol, Iran

E-mail:
khaliliasbo@yahoo.com
salehisss@baboliau.ac.ir

Abstract: Let $G$ be a finite group. The main supergraph $\mathcal{S}(G)$ is a graph with vertex set $G$ in which two vertices $x$ and $y$ are adjacent if and only if $o(x) \mid o(y)$ or $o(y)\mid o(x)$. In this paper, we will show that $G\cong Sz(q)$ if and only if $\mathcal{S}(G)\cong \mathcal{S}(Sz(q))$, where $q=2^{2m+1}\ge 8$.

AMSclassification: primary 20D08; secondary 05C25.

Keywords: main supergraph, Suzuki group.

DOI: 10.5817/AM2019-4-225