“School of Mathematics”
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Paper IPM / M / 16528  


Abstract:  
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 nonsolvable 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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