Sylow子群个数和较少的有限非可解群
Finite Non-Solvable Groups with Few Sum of Numbers of Sylow Subgroups
DOI: 10.12677/PM.2026.163075, PDF,    国家自然科学基金支持
作者: 李婷婷：湖北民族大学数学与统计学院，湖北 恩施
关键词: Sylow 数；极大正规子群；非交换单群；Sylow Number； Maximal Normal Subgroup； Non-Abelian Simple Groups
摘要: 设G是一个有限群且np(G)是G的Sylow p-子群的个数. 设S(G)={p∈π(G): np(G) > 1}且定义δ0(G)=∑p∈S(G)np(G). Sol(G) 表示可解根. 在这篇论文中, 如果 G 是一个非可解群且δ0(G) ≤ 1000, 我们完全分类了 G/Sol(G)。
Abstract: Let G be a finite group and np(G) be the number of Sylow p-subgroups of G. Let S(G)={p∈π(G): np(G) > 1} and define δ0(G)=∑p∈S(G)np(G). Denote by Sol(G) the solvable radical. In this paper, if G is non-solvable and δ0(G) ≤ 1000, we classify G/Sol(G) completely.
文章引用：李婷婷. Sylow子群个数和较少的有限非可解群[J]. 理论数学, 2026, 16(3): 112-121. https://doi.org/10.12677/PM.2026.163075

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