有限群的s-半置换子群
Finite Groups with Some s-Semipermutable Subgroups
DOI: 10.12677/AAM.2024.137308, PDF, 下载: 13  浏览: 19  国家自然科学基金支持
作者: 徐向阳, 刘小伟：南昌师范学院数学与信息科学学院，江西 南昌；李样明*：广东第二师范学院数学学院，广东 广州
关键词: s-半置换子群；Sylow p-子群；p- 超可解群；最小生成元数；s-Semipermutable Subgroup； Sylow p-Subgroup； p-Supersoluble Sroup； Minimum Generative Element
摘要: 设G为有限群， H为G的子群。 若对G的任意满足(|P |, |H|) = 1的Sylow 子群P ， 都有GpH = HGp成立，则称H为G的s-半置换子群。 本文，我们主要探究具有若干s-半置换子群的有限群的结构。 我们的结论推广了前人的若干结果。
Abstract: Suppose that G is a finite group and H is a subgroup of G. We say that H is s- semipermutable in G if HGp = GpH for any Sylow p-subgroup Gp of G with (p, |H|) = 1. We investigate the influence of s-semipermutable subgroups on the structure of finite groups. Some recent results are generalized.
文章引用：徐向阳, 李样明, 刘小伟. 有限群的s-半置换子群[J]. 应用数学进展, 2024, 13(7): 3220-3226. https://doi.org/10.12677/AAM.2024.137308

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