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

 

The intersection of Sylow subgroups


Author: Avionam Mann
Journal: Proc. Amer. Math. Soc. 53 (1975), 262-264
MSC: Primary 20D10
Addendum: Proc. Amer. Math. Soc. 62 (1977), 188.
MathSciNet review: 0384924
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Abstract: Let $ G$ be a finite soluble group. If the order of $ G$ is not divisible by any Fermat or Mersenne primes, then there exist Sylow $ 2$-subgroups, $ P$ and $ Q$, such that $ P \cap Q = {O_p}(G)$. This improves on a result of Itô. A similar result is proved for nilpotent injectors.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1975-0384924-5
PII: S 0002-9939(1975)0384924-5
Article copyright: © Copyright 1975 American Mathematical Society