 

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, nonsolvable, main supergraph, Thompson's problem. 
Subject [2010]: 
20D08, 05C25. 


Abstract
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 nonsolvable groups, then G ≅ S. This work is an important
step in solving Thompson's problem.


Acknowledgements
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
a.khalili@cfu.ac.ir
Seyed Sadegh Salehi Amiri:
Department of Mathematics
Babol Branch, Islamic Azad University
Babol, Iran
salehisss@baboliau.ac.ir

