The Normalizer Property for Finite GroupsWhose Sylow 2-Subgroups are Abelian

In this paper we mainly investigate the Coleman automorphisms and class-preserving automorphisms of finite AZ-groups and finite groups related to AZ-groups.For example,we first prove that Outc(G)of an AZ-group G must be a 2′-group and therefore the normalizer property holds for G.Then we find some classes of finite groups such that the intersection of their outer class-preserving automorphism groups and outer Coleman automorphism groups is 2′-groups,and therefore,the normalizer property holds for these kinds of finite groups.Finally,we show that the normalizer property holds for the wreath products of AZ-groups by rational permutation groups under some conditions.