Nonsolvable Groups with no Prime Dividing Four Character Degrees |
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Authors: | Mehdi Ghaffarzadeh Mohsen Ghasemi Mark L Lewis Hung P Tong-Viet |
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Institution: | 1.Department of Mathematics,Khoy Branch, Islamic Azad University,Khoy,Iran;2.Department of Mathematics,Urmia University,Urmia,Iran;3.Department of Mathematical Sciences,Kent State University,Kent,USA |
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Abstract: | Given a finite group G, we say that G has property \(\mathcal P_{k}\) if every set of k distinct irreducible character degrees of G is setwise relatively prime. In this paper, we show that if G is a finite nonsolvable group satisfying \(\mathcal P_{4}, \)then G has at most 8 distinct character degrees. Combining with work of D. Benjamin on finite solvable groups, we deduce that a finite group G has at most 9 distinct character degrees if G has property \(\mathcal P_{4}\) and this bound is sharp. |
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