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Paper   IPM / M / 16528
School of Mathematics
  Title:   Non-solvable groups having five irreducible character degrees
  Author(s):  Farideh Shafiei (Joint with K. Aziziheris and F. Shirjian)
  Status:   To Appear
  Journal: Comm. Algebra
  Supported by:  IPM
Let G be a finite group and let cd(G) be the set of degrees of complex irreducible characters of G. An important program in character theory is to obtain the structure of G when cd(G) is known. In this paper, we consider a dual version of this approach. Indeed, we consider non-solvable groups with 5 character degrees and present a description of the set of character degrees for such groups. As an application of this result, it is shown that a finite group with 5 character degrees and containing no prime power must be a solvable group.

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