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Nonsolvable Groups Satisfying the One-prime Hypothesis

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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.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Kent State University, Kent, OH, 44242, USA

    Mark L. Lewis & Donald L. White

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  1. Mark L. Lewis
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  2. Donald L. White
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Correspondence to Mark L. Lewis.

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Lewis, M.L., White, D.L. Nonsolvable Groups Satisfying the One-prime Hypothesis. Algebr Represent Theor 10, 379–412 (2007). https://doi.org/10.1007/s10468-007-9057-2

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