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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


A note on Sylow intersections

Author: Ariel Ish-Shalom
Journal: Proc. Amer. Math. Soc. 66 (1977), 227-230
MSC: Primary 20D20
MathSciNet review: 0460460
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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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PII: S 0002-9939(1977)0460460-4
Article copyright: © Copyright 1977 American Mathematical Society

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