Class-Preserving Coleman Automorphisms of Finite Groups Whose Second Maximal Subgroups Are TI-Subgroups

Recall that a subgroup H of a finite group G is called a TI-subgroup if H \H g = 1 or H for each g 2 G. Suppose that G is a finite group whose second maximal subgroups are TI-subgroups. It is shown that every class-preserving Coleman automorphism of G is an inner automorphism. As an immediate consequence of this result, we obtain that the normalizer property holds for G.