Nonsolvable Groups Satisfying the One-prime Hypothesis |
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Authors: | Mark L. Lewis Donald L. White |
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Affiliation: | (1) Department of Mathematical Sciences, Kent State University, Kent, OH 44242, USA |
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Abstract: | Recall that a finite group G satisfies the one-prime hypothesis if the greatest common divisor for any pair of distinct degrees in cd(G) is either 1 or a prime. In this paper, we classify the nonsolvable groups that satisfy the one-prime hypothesis. As a consequence of our classification, we show that if G is a nonsolvable group satisfying the one-prime hypothesis, then |cd(G)| ≤ 8, and hence, if G is any group satisfying the one-prime hypothesis, then |cd(G)| ≤ 9. Presented by Don Passman. |
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Keywords: | One-prime hypothesis Finite group Irreducible characters |
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