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The Normalizer Property for Finite Groups Whose Sylow 2-Subgroups are Abelian
Communications in Mathematics and Statistics ( IF 1.1 ) Pub Date : 2020-10-01 , DOI: 10.1007/s40304-020-00211-w
Tao Zheng , Xiuyun Guo

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.



中文翻译:

Sylow 2-子群为Abelian的有限群的Normalizer属性

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。

更新日期:2020-10-02
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