On Thompson's conjecture for finite simple exceptional groups of Lie type

TL;DR

This paper proves that a finite group with trivial center is uniquely determined by its set of conjugacy classes if it is a finite simple exceptional Lie type group or Tits group, confirming Thompson's conjecture in this context.

Contribution

It establishes that finite simple exceptional Lie type groups are uniquely characterized by their conjugacy class sets, confirming Thompson's conjecture for these groups.

Findings

Finite simple exceptional Lie type groups are uniquely identified by their conjugacy class sets.

Thompson's conjecture holds for finite simple groups of exceptional Lie type and Tits group.

The result applies to groups with trivial center, ensuring uniqueness.

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 of exceptional Lie type or Tits group.