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

Behrooz Khosravi, Behnam Khosravi, Bahman Khosravi, Zahra Momen (2015)

Czechoslovak Mathematical Journal

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

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