Characterization of PSL(2,11) by the set U(G)

TL;DR

This paper proves that any finite simple group sharing the same conjugacy class set as PSL(2, 11) must be isomorphic to PSL(2, 11), thus characterizing the group uniquely by its conjugacy class set.

Contribution

The paper provides a characterization of PSL(2, 11) among finite simple groups using the set of conjugacy class sizes, establishing a uniqueness result.

Findings

Any finite simple group with the same conjugacy class set as PSL(2, 11) is isomorphic to it.

The conjugacy class set U(G) uniquely determines PSL(2, 11) among finite simple groups.

Abstract

In this paper, we prove that if G is a finite simple group with the same-size conjugacy class set U(G) = U(PSL(2, 11)), then G is isomorphic to PSL(2, 11).