JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2024, Vol. 59 ›› Issue (4): 23-30.doi: 10.6040/j.issn.1671-9352.0.2023.252

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Smooth skew morphisms of a kind of maximal class 3-groups which have abelian maximal subgroups

Jianji CAO(),Junxin WANG*(),Pengfei BAI   

  1. School of Applied Mathematics, Shanxi University of Finance and Economics, Taiyuan 030006, Shanxi, China
  • Received:2023-06-05 Online:2024-04-20 Published:2024-04-12
  • Contact: Junxin WANG E-mail:13994371056@163.com;wangjunxin660712@163.com

Abstract:

A skew morphism φ of a finite group G is a permutation of G fixing the identity of G and satisfying the property φ(gh)=φ(g)φπ(g)(h) for any g, hG, where π is a function from G to {1, 2, …, d-1} for the order d of φ. If for any gG, π(g)=1, then φ is an automorphism of G. Hence a skew morphism is a generalization of an automorphism. When π(φ(g))=π(g) for any gG, the skew morphism φ is called a smooth skew morphism. In this paper, we classify all smooth skew morphisms of a kind of maximal class 3-groups which have abelian maximal subgroups.

Key words: maximal class 3-group, smooth skew morphism, regular Cayley map, skew morphism, maximal subgroup

CLC Number: 

  • O152.1
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