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Groups with central $2$-Sylow intersections of rank at most one
Proceedings of the American Mathematical Society
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. Previous results. Of basic importance is Theorem 2.1. Let z be a central involution in G. Suppose z lies in no proper 2-Sylow intersectiondoi:10.1090/s0002-9939-1973-0430055-3 fatcat:txef77ltlvhzfnzxpdk2ecs4dq