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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Projective groups of degree less than $ 4p/3$ where centralizers have normal Sylow $ p$-subgroups


Author: J. H. Lindsey
Journal: Trans. Amer. Math. Soc. 175 (1973), 233-247
MSC: Primary 20D20
MathSciNet review: 0310056
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Abstract: This paper proves the following theorem:

Theorem 1. Let $ \bar G$ be a finite primitive complex projective group of degree n with a Sylow p-subgroup $ \bar P$ of order greater than p for p prime greater than five. Let $ n \ne p,n < 4p/3$, and if $ p = 7,n \leqslant 8$. Then $ p \equiv 1 \pmod 4,\bar P$ is a trivial intersection set, and for some nonidentity element $ \bar x\;in\;\bar G,C(\bar x)$ does not have a normal Sylow p-subgroup.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1973-0310056-0
PII: S 0002-9947(1973)0310056-0
Keywords: Primitive projective group, trivial intersection set, centralizers having normal Sylow p-subgroups
Article copyright: © Copyright 1973 American Mathematical Society