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 \(Out_c(G)\) 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.

在本文中，我们主要研究有限AZ群和与AZ群有关的有限群的Coleman自同构和保类自同构。例如，我们首先证明\（OUT_C（G）\）的的AZ -基ģ必须是\（2' \） -基团，因此归一化属性保存为G ^。然后我们找到了一些有限群类，使得它们的外部类保留自同构群和外部Coleman自同构群的交集为\（2'\） -群，因此，归一化器属性对于这类有限群成立。最后，我们证明归一化属性对于在某些条件下，由有理置换组组成的AZ-组。