指数非素数方幂的极大子群对群结构的影响

吉林大学学报(理学版) ›› 2026, Vol. 64 ›› Issue (4): 801-0808.

指数非素数方幂的极大子群对群结构的影响

常敬新¹, 缪龙¹, 周文霞¹, 王春花^1,2

1. 河海大学数学学院, 南京 211100； 2. 马鞍山职业技术学院基础部, 安徽马鞍山 243031

收稿日期:2025-11-11 出版日期:2026-07-26 发布日期:2026-07-26
通讯作者: 缪龙 E-mail:20210088@hhu.edu.cn

Influence of Maximal Subgroups with Non-prime-power Indices on Group Structure

Chang Jingxin¹, Miao Long¹, Zhou Wenxia¹, Wang Chunhua^1,2

1. School of Mathematics, Hohai University, Nanjing 211100, China；2. Department of Foundation, Ma’anshan Technical College, Ma’anshan 243031, Anhui Province, China

Received:2025-11-11 Online:2026-07-26 Published:2026-07-26

摘要/Abstract

摘要： 基于极大子群的指数特征, 构建指数非素数方幂的极大子群集合, 给出与之相关的二极大子群的分类, 并结合其强弱性以及阶的奇偶性对群结构进行深入讨论, 得到了群属于相关群系的若干充分条件.

关键词: 指数非素数方幂的极大子群, 二极大子群, 非可解群, 群系

Abstract: Based on the index properties of maximal subgroups, we constructed a set of maximal subgroups with non-prime-power indices, provided some classifications of the associated second maximal subgroups, and discussed the structure of the group in depth by combining their strength and parity of the orders, obtaining several sufficient conditions for a group to belong to the related formations.

Key words: maximal subgroups with non-prime-power index, second maximal subgroup, non-solvable group, formation

中图分类号:

O152.1

常敬新, 缪龙, 周文霞, 王春花. 指数非素数方幂的极大子群对群结构的影响[J]. 吉林大学学报(理学版), 2026, 64(4): 801-0808.

Chang Jingxin, Miao Long, Zhou Wenxia, Wang Chunhua. Influence of Maximal Subgroups with Non-prime-power Indices on Group Structure[J]. Journal of Jilin University Science Edition, 2026, 64(4): 801-0808.

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