Skew-morphisms of cyclic 2-groups-Reference-Cited by-同舟云学术

Skew-morphisms of cyclic 2-groups

Published:2019-03-08 Issue:4 Volume:22 Page:617-635
ISSN:1435-4446
Container-title:Journal of Group Theory
language:en
Short-container-title:

Author:

Du Shaofei¹,Hu Kan²

Affiliation:

1. School of Mathematical Sciences , Capital Normal University , Beijing 100048 , P. R. China

2. School of Mathematics, Physics and Information Science , Zhejiang Ocean University , Zhoushan , Zhejiang 316022 ; and Key Laboratory of Oceanographic Big Data Mining & Application of Zhejiang Province, Zhoushan, Zhejiang 316022 , P. R. China

Abstract

Abstract A skew-morphism of a finite group A is a permutation φ on A fixing the identity element, and for which there exists an integer function π on A such that, for all x , y ∈ A

{x,y\in A}

, φ ⁢ ( x ⁢ y ) = φ ⁢ ( x ) ⁢ φ π ⁢ ( x ) ⁢ ( y )

{\varphi(xy)=\varphi(x)\varphi^{\pi(x)}(y)}

. In [I. Kovács and R. Nedela, Skew-morphisms of cyclic p-groups, J. Group Theory 20 2017, 6, 1135–1154], Kovács and Nedela determined skew-morphisms of the cyclic p-groups for any odd prime p. In this paper, we shall determine that of cyclic 2-groups.

Funder

National Natural Science Foundation of China

Natural Science Foundation of Zhejiang Province

Department of Education of Zhejiang Province

Publisher

Walter de Gruyter GmbH

Subject

Algebra and Number Theory

Reference18 articles.

1. M. Bachratý and R. Jajcay, Powers of skew-morphisms, Symmetries in Graphs, Maps, and Polytopes, Springer Proc. Math. Stat. 159, Springer, Cham (2016), 1–25.

2. M. Bachratý and R. Jajcay, Classification of coset-preserving skew-morphisms of finite cyclic groups, Australas. J. Combin. 67 (2017), 259–280.

3. M. D. E. Conder, R. Jajcay and T. W. Tucker, Cyclic complements and skew morphisms of groups, J. Algebra 453 (2016), 68–100.

4. M. D. E. Conder and T. W. Tucker, Regular Cayley maps for cyclic groups, Trans. Amer. Math. Soc. 366 (2014), no. 7, 3585–3609.

5. J. Douglas, On the supersolvability of bicyclic groups, Proc. Natl. Acad. Sci. USA 47 (1961), 1493–1495.

Cited by 9 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Regular dessins with underlying graphs K2e,2f: The metacyclic case;Discrete Mathematics;2024-07

2. Skew-morphisms of elementary abelian -groups;Journal of Group Theory;2024-05-07

3. Classification of cyclic groups underlying only smooth skew morphisms;Journal of Algebraic Combinatorics;2024-04-03

4. REGULAR t-BALANCED CAYLEY MAPS ON SPLIT METACYCLIC 2-GROUPS;B KOREAN MATH SOC;2024

5. Quotients of skew morphisms of cyclic groups;Ars Mathematica Contemporanea;2023-10-04