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Some Character Degree Conditions Implying Solvability of Finite Groups |
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| Authors: | Kamal Aziziheris |
| Institution: | 1. Department of Mathematical Sciences, University of Tabriz, Tabriz, Iran 2. School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P.O.Box 19395-5746, Tehran, Iran 3. Department of Mathematics, Texas State University, 601 University Drive, San Marcos, TX, 78666, USA |
| Abstract: | Let cd(G) be the set of all irreducible complex character degrees of a finite group G. In this paper, we show that if a, b, and c are pairwise relatively prime integers and ${\rm{cd}} \left(G\right) \subseteq \{1, a, b, c, ab, ac\}$ , then either G is solvable or {a, b, c}?=?{2 f ???1, 2 f , 2 f ?+?1} for some $f \geqslant 2$ and cd (G)?=?{1, a, b, c}. |
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