Smooth skew morphisms of dihedral groups

被引：12
作者：
Wang, Na-Er [1 ,2 ]
Hu, Kan [1 ,2 ]
Yuan, Kai [3 ]
Zhang, Jun-Yang [4 ]
机构：
[1] Zhejiang Ocean Univ, Dept Math, Zhoushan 316022, Zhejiang, Peoples R China
[2] Key Lab Oceanog Big Data Min & Applicat Zhejiang, Zhoushan 316022, Zhejiang, Peoples R China
[3] Capital Normal Univ, Sch Math, Beijing 100037, Peoples R China
[4] Chongqing Normal Univ, Sch Math Sci, Chongqing 401331, Peoples R China
来源：
ARS MATHEMATICA CONTEMPORANEA | 2019年 / 16卷 / 02期
基金：
中国国家自然科学基金;
关键词：
Cayley map; skew morphism; smooth subgroup; REGULAR CAYLEY MAPS; CLASSIFICATION;
D O I：
10.26493/1855-3974.1475.3d3
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A skew morphism phi of a finite group A is a permutation on A fixing the identity element of A and for which there exists an integer-valued function pi on A such that phi(ab) = phi(a)phi(pi(a))(b) for all a, b is an element of A. In the case where pi(phi(a)) = pi(a), for all a is an element of A, the skew morphism is smooth. The concept of smooth skew morphism is a generalization of that of t-balanced skew morphism. The aim of this paper is to develop a general theory of smooth skew morphisms. As an application we classify smooth skew morphisms of dihedral groups.
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页码：527 / 547
页数：21
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