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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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Counting group elements of order $p$ modulo $p^{2}$
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by Marcel Herzog PDF
Proc. Amer. Math. Soc. 66 (1977), 247-250 Request permission

Abstract:

Let G be a finite group of order divisible by the prime p. It is shown that the number of elements of G of order p is congruent to $- 1$ modulo ${p^2}$, unless a Sylow p-subgroup of G is cyclic, generalized quaternion, dihedral or quasidihedral.
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Additional Information
  • © Copyright 1977 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 66 (1977), 247-250
  • MSC: Primary 20D99
  • DOI: https://doi.org/10.1090/S0002-9939-1977-0466316-5
  • MathSciNet review: 0466316