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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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A note on Sylow intersections
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by Ariel Ish-Shalom PDF
Proc. Amer. Math. Soc. 66 (1977), 227-230 Request permission

Abstract:

Let p be a prime number, G a finite group whose order is divisible by p, and S a Sylow p-subgroup of G. We say that G satisfies $( \ast )$ if there exists $g \in G$ such that $S \cap {S^g} = {O_p}(G)$. There are examples of primes p and finite groups G that do not satisfy $( \ast )$. In this note we discuss several related properties satisfied in general, as well as giving sufficient conditions for G to satisfy $( \ast )$.
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Additional Information
  • © Copyright 1977 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 66 (1977), 227-230
  • MSC: Primary 20D20
  • DOI: https://doi.org/10.1090/S0002-9939-1977-0460460-4
  • MathSciNet review: 0460460