CharacterizationofP SU(3,q)byitsorderandonespecialconjugacyclasssize

Abstract

Suppose that G be a finite group, and let N (G)be the set of conjugacy class sizes of G. By Thompson’s conjecture, if H is a finite non abelian simple group, G is a finite group with a trivial center, and N (G) = N (H), then H and G are isomorphic. Chen et al. contributed interestingly to Thompsons conjecture under a weak condition. In this article, we investigate validity of Thompsons conjecture under a weak condition for the projective special unitary groups. This work implies that Thompsons conjecture holds for the PSU (3, q), where q is prime power.