Groups with central 2-Sylow intersections of rank at most one

Herzog, Marcel; Shult, Ernest

doi:10.1090/S0002-9939-1973-0430055-3

Groups with central $2$-Sylow intersections of rank at most one
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by Marcel Herzog and Ernest Shult PDF

Proc. Amer. Math. Soc. 38 (1973), 465-470 Request permission

Abstract:

An involution in a finite group is called central if it lies in the center of a $2$-Sylow subgroup of $G$. A $2$-Sylow intersection is called central if it is either trivial or contains a central involution. Suppose $G$ is a finite simple group all of whose central $2$-Sylow intersections are trivial or rank one $2$-groups. It is proved that $G$ is a known simple group.

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