Class-preserving coleman automorphisms of permutational wreath products with 2-closed base groups

被引：0
|
作者：
Li, Zhengxing [1 ,2 ]
Li, Yuanlin [3 ]
机构：
[1] Qingdao Univ, Coll Math, Qingdao 266071, Shandong, Peoples R China
[2] Qingdao Univ, Coll Automat Engn, Qingdao 266071, Shandong, Peoples R China
[3] Brock Univ, Dept Math & Stat, St Catharines, ON L2S 3A1, Canada
来源：
JOURNAL OF ALGEBRA AND ITS APPLICATIONS | 2016年 / 15卷 / 10期
基金：
中国国家自然科学基金; 高等学校博士学科点专项科研基金;
关键词：
Class-preserving Coleman automorphism; the normalizer property; permutational wreath product; INTEGRAL GROUP-RINGS; NORMALIZER PROPERTY;
D O I：
10.1142/S0219498816501899
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Let N be a nontrivial 2-closed group and let H be an arbitrary permutation group on a finite set Omega. Let G = N (sic) H be the corresponding permutational wreath product of N by H. It is shown that every class-preserving Coleman automorphism of 2-power order of G is inner. As a direct consequence, it is obtained that the normalizer property holds for G. Further, it is shown that every class-preserving Coleman automorphism of G is inner whenever N is nilpotent. Our results generalize some known ones.
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页数：11
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