A new characterization for the simple group PSL(2, p²) by order and some character degrees

چکیده مقاله

Let G be a finite group and p a prime number. We prove that if G is a finite group of order |PSL(2, p²)| such that G has an irreducible character of degree p² and we know that G has no irreducible character θ such that 2p | θ(1), then G is isomorphic to PSL(2, p²). As a consequence of our result we prove that PSL(2, p²) is uniquely determined by the structure of its complex group algebra. © 2015, Institute of Mathematics of the Academy of Sciences of the Czech Republic, Praha, Czech Republic.