Let be a finite group and be the set of all irreducible complex character degrees of counting multiplicities.
Let be an odd prime number and M = PGL(2,p), M = Z2xPSL(2,p) or . In this paper we prove that is uniquely determined by its order and some information on its character degrees. As a consequence of our results we prove that if is a finite group such that , then . This implies that is uniquely determined by the structure of its complex group algebra.
Key Words: Character degrees, order, projective special linear group, characterization
2010 Mathematics Subject Classification: Primary 20C15
Secondary 20D05, 20D60
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