The characterization of PSL(2, p) (p≡±5 (mod 24))

Abstract

Let G be a finite group. A vanishing element of G is an element g ∈ G such that χ ( g ) = 0 for some irreducible complex character χ of G. We will denote by Van(G) the set of vanishing elements of G and by Vo ( G ) the set of the order of elements in Van ( G ) . For certain specified primes p that satisfy p ≡ ± 5 ( mod 24 ) , if Vo ( G ) = Vo ( PSL ( 2 , p ) ) , then G ≅ PSL ( 2 , p ) .