A New Characterization of PSL(3; q)

Abstract

In this paper, we will show that the simple group PSL(3, q) can be uniquely characterized by order and one conjugacy class length, where q is a prime power. A main consequence of our result is the validity of Thompson's conjecture under a weak condition for the group under consideration.

Key words and phrases. Conjugacy class length, Prime graph, Thompson's conjecture.

2000 Mathematics Subject Classification. 20D08, 20D60