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

Lindsey, J. H.

doi:10.1090/S0002-9947-1973-0310056-0

Projective groups of degree less than $4p/3$ where centralizers have normal Sylow $p$-subgroups
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Trans. Amer. Math. Soc. 175 (1973), 233-247 Request permission

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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Über eine Klasse von endlichen Gruppen linearer Substitutionen