Class-Preserving Coleman Automorphisms of Finite Groups with Prescribed Centralizers

被引：0
|
作者：
Li, Zhengxing [1 ,2 ]
Gao, Hongwei [2 ,3 ]
机构：
[1] Qingdao Univ, Coll Automat & Elect Engn, Qingdao 266071, Shandong, Peoples R China
[2] Qingdao Univ, Sch Math & Stat, Qingdao 266071, Shandong, Peoples R China
[3] Inst Appl Math Shandong, Qingdao 266071, Shandong, Peoples R China
来源：
ALGEBRA COLLOQUIUM | 2017年 / 24卷 / 02期
基金：
高等学校博士学科点专项科研基金; 中国博士后科学基金; 中国国家自然科学基金;
关键词：
class-preserving automorphism; Coleman automorphism; integral group ring; the normalizer conjecture; INTEGRAL GROUP-RINGS; NORMALIZER PROPERTY;
D O I：
10.1142/S1005386717000219
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Let G be a finite group. It is proved that any class-preserving Coleman automorphism of G is an inner automorphism whenever G belongs to one of the following two classes of groups: (1) CN-groups, i.e., groups in which the centralizer of any element is nilpotent; (2) CIT-groups, i.e., groups of even order in which the centralizer of any involution is a 2-group. In particular, the normalizer conjecture holds for both CN-groups and CIT-groups. Additionally, some other results are also obtained.
引用
收藏
页码：351 / 360
页数：10
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