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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Prime factors of conjugacy classes of finite solvable groups
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by Pamela A. Ferguson PDF
Proc. Amer. Math. Soc. 113 (1991), 319-323 Request permission

Abstract:

A bound for the number of primes dividing $[G:Z(G)]$ for certain finite solvable groups $G$ is given in terms of the maximal number of primes dividing a conjugacy class.
References
    D. Chillag and M. Herzog, On the lengths of conjugacy classes of finite groups, private correspondence.
  • David Gluck, A conjecture about character degrees of solvable groups, J. Algebra 140 (1991), no. 1, 26–35. MR 1114902, DOI 10.1016/0021-8693(91)90142-U
  • P. Ferguson, Connections between prime divisors of conjugacy classes and prime divisors of $|G|$, J. Algebra (to appear).
  • Daniel Gorenstein, Finite groups, Harper & Row, Publishers, New York-London, 1968. MR 0231903
  • Marshall Hall Jr., The theory of groups, The Macmillan Company, New York, N.Y., 1959. MR 0103215
  • Olaf Manz, Endliche auflösbare Gruppen, deren sämtliche Charaktergrade Primzahlpotenzen sind, J. Algebra 94 (1985), no. 1, 211–255 (German). MR 789547, DOI 10.1016/0021-8693(85)90210-8
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Additional Information
  • © Copyright 1991 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 113 (1991), 319-323
  • MSC: Primary 20D10; Secondary 20C15
  • DOI: https://doi.org/10.1090/S0002-9939-1991-1049135-8
  • MathSciNet review: 1049135