Vol. 45, No. 2, 1973

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Central 2-Sylow intersections

Marcel Herzog

Vol. 45 (1973), No. 2, 535–538

Let G be a finite group. A subgroup D of G is called a 2-Sylow intersection if there exist distinct Sylow 2-subgroups S1 and S2 of G such that D = S1 S2. An involution of G is called central if it is contained in a center of a Sylow 2-subgroup of G. A 2-Sylow intersection is called central if it contains a central involution. The aim of this work is to determine all non-abelian simple groups G which satisfy the following condition

B: the 2-rank of all centra12-Sylow intersections is not higher than 1, under the additional assumption that the centralizer of a central involution of G is solvable.

Mathematical Subject Classification 2000
Primary: 20D20
Received: 6 December 1971
Published: 1 April 1973
Marcel Herzog