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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Counting $p$-subgroups
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by Ernst Snapper
Proc. Amer. Math. Soc. 39 (1973), 81-82
DOI: https://doi.org/10.1090/S0002-9939-1973-0314972-0
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Abstract:

There are many theorems which state that the number of $p$-subgroups of a finite group, where these $p$-subgroups satisfy varying conditions, is congruent $1\operatorname {modulo} p$. We derive here a simple theorem which has all these special theorems as corollaries.
References
  • W. Burnside, Theory of groups of finite order, Dover Publications, Inc., New York, 1955. 2d ed. MR 0069818
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Bibliographic Information
  • © Copyright 1973 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 39 (1973), 81-82
  • MSC: Primary 20D20
  • DOI: https://doi.org/10.1090/S0002-9939-1973-0314972-0
  • MathSciNet review: 0314972