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.
