Class-preserving Coleman automorphisms of finite AQTI-groups

A subgroup H of a finite group G is called a QTI-subgroup if C_G(x) ≤ N_G(H) for any 1 ≠ x ∈ H. Let G be an AQTI-group, i.e. a group all of whose abelian subgroups are QTI-subgroups. It is shown that every class-preserving Coleman automorphism of G is an inner automorphism. As an immediate consequence, we obtain that the normalizer property holds for such groups G.