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Variations on average character degrees and p-nilpotence

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Abstract

We prove that if p is an odd prime, G is a solvable group, and the average value of the irreducible characters of G whose degrees are not divisible by p is strictly less than 2(p + 1)/(p + 3), then G is p-nilpotent. We show that there are examples that are not p-nilpotent where this bound is met for every prime p. We then prove a number of variations of this result.

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Authors and Affiliations

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

    Mark L. Lewis

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  1. Mark L. Lewis
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Correspondence to Mark L. Lewis.

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Lewis, M.L. Variations on average character degrees and p-nilpotence. Isr. J. Math. 215, 749–764 (2016). https://doi.org/10.1007/s11856-016-1393-7

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  • DOI: https://doi.org/10.1007/s11856-016-1393-7

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