New York Journal of Mathematics
Volume 28 (2022), 1057-1063


Alireza Khalili Asboei and Seyed Sadegh Salehi Amiri

The main supergraph of finite groups

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Published: July 27, 2022.
Keywords: same order type groups, non-solvable, main supergraph, Thompson's problem.
Subject [2010]: 20D08, 05C25.

Let G be a finite group. The main supergraph S(G) is a graph with vertex set G in which two vertices x and y are adjacent if and only if o(x) | o(y) or o(y) | o(x). In this paper, we will show that if S(G) ≅ S(S), where S belongs to a large class of finite non-solvable groups, then G ≅ S. This work is an important step in solving Thompson's problem.


We thank the referee for some extremely helpful remarks, which allowed us to improve the paper.

Author information

Alireza Khalili Asboei:
Department of Mathematics
Farhangian University
Tehran, Iran


Seyed Sadegh Salehi Amiri:
Department of Mathematics
Babol Branch, Islamic Azad University
Babol, Iran