Re-characterization of PGL(2, p) by its order and one class length

Abstract

The present article used the classification of simple groups to prove that group G is isomorphic to the projective linear group P G L(2, p) if |G| = p(p 2 − 1) and p 2 − 1 ∈ N (G), where N (G) is the collection of conjugacy class length of G and p is a prime.