蕴含交换极大子群的极大类3-群上的光滑斜态射

doi:10.6040/j.issn.1671-9352.0.2023.252

《山东大学学报(理学版)》 ›› 2024, Vol. 59 ›› Issue (4): 23-30.doi: 10.6040/j.issn.1671-9352.0.2023.252

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蕴含交换极大子群的极大类3-群上的光滑斜态射

曹建基,王俊新^*,白鹏飞

山西财经大学应用数学学院, 山西太原 030006

发布日期:2024-04-12
通讯作者: 王俊新(1966— ),男,教授,博士,研究方向为有限群论. E-mail:wangjunxin660712@163.com
基金资助:
国家自然科学基金资助项目(12171302,11801334,12061030);山西省自然科学基金资助项目(202103021224287);山西省高等学校科技创新资助项目(2021L278)

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

CAO Jianji, WANG Junxin^*, BAI Pengfei

School of Applied Mathematics, Shanxi University of Finance and Economics, Taiyuan 030006, Shanxi, China

Published:2024-04-12

摘要/Abstract

摘要： 一个有限群G上的斜态射为G的一个置换φ,满足φ(1)=1且φ(gh)=φ(g)φ^π(g)(h)对任意g,h∈G均成立,其中π为G到集合{1,2,…,d-1}的一个函数且d为φ的阶。若对任意的g∈G都有π(g)=1,则φ为G的自同构。因此斜态射为群的自同构的推广。若对任意g∈G都有π(φ(g))=π(g),则斜态射φ被称为光滑斜态射。本文研究了一类蕴含交换极大子群的极大类3-群上的光滑斜态射,并给出了其完全分类。

关键词: 极大类3-群, 光滑斜态射, 正则凯莱地图, 斜态射, 极大子群

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)φ^π(g)(h) for any g,h∈G, where π is a function from G to {1,2,…,d-1} for the order d of φ. If for any g∈G, 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 g∈G, 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

中图分类号:

O152.1

曹建基,王俊新,白鹏飞. 蕴含交换极大子群的极大类3-群上的光滑斜态射[J]. 《山东大学学报(理学版)》, 2024, 59(4): 23-30.

CAO Jianji, WANG Junxin, BAI Pengfei. Smooth skew morphisms of a kind of maximal class 3-groups which have abelian maximal subgroups[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2024, 59(4): 23-30.

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蕴含交换极大子群的极大类3-群上的光滑斜态射

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

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