On Thompson's conjecture for finite simple groups

TL;DR

This paper proves that a finite group with a trivial center is uniquely determined by its set of conjugacy classes, specifically identifying it as a finite simple group if the sets match.

Contribution

It establishes that finite groups with trivial centers are uniquely characterized by their conjugacy class sets, confirming Thompson's conjecture for finite simple groups.

Findings

Finite groups with trivial centers are uniquely identified by their conjugacy class sets.

If two such groups have identical conjugacy class sets, they are isomorphic.

The result confirms Thompson's conjecture for finite simple groups.

Abstract

Let $G$ be a finite group, $N(G)$ be the set of conjugacy classes of the group $G$. In the present paper it is proved $G\simeq L$ if $N(G)=N(L)$, where $G$ is a finite group with trivial center and $L$ is a finite simple group.