指数非素数方幂的极大子群对群结构的影响

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

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.

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.

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

Key words

maximal subgroups with non-prime-power index / second maximal subgroup / non-solvable group / formation

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基金资助

国家自然科学基金(12371018)

中央高校基本科研业务费专项基金(2013/B240201093)

安徽省高等学校自然科学类研究项目(2024AH051789)