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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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DOI: http://dx.doi.org/10.1090/S0002-9939-1977-0460460-4
Article copyright: © Copyright 1977 American Mathematical Society