准素数阶子群的弱Φ-可补
Weakly Φ-Supplemented Subgroups of Prime Power Order
DOI: 10.12677/PM.2018.84046, PDF,    国家科技经费支持
作者: 谢凤艳*：安阳学院建筑工程学院，河南 安阳；尚华辉：永城职业学院基础部，河南 永城
关键词: 弱Φ-可补子群；ρ-幂零群；Sylow-子群；WeaklyΦ-Supplemented Subgroups； ρ-Nilpotent Groups； Sylow Subgroups
摘要: 设G是一个群，H是G的子群。称H在G中弱Φ-可补，若G中存在一个子群T使得G = HT且H ∩ T ≤ Φ(H), 其中Φ(H)为H的Frattini子群。本文给出弱Φ-可补的概念并利用群G的某些素数幂阶子群的弱Φ-可补子性给出群G的一些性质和结构。
Abstract: Let G be group and H a subgroup of G. We say H is weaklyΦ-supplemented in G if G has a subgroup T such that G = HT and H ∩ T ≤ Φ(H), where Φ(H) is Frattini subgroup of H. In this paper, new results of the structure and properties of a finite group G are given, providing that some subgroups of prime power order are weakly Φ-supplemented in G.
文章引用：谢凤艳, 尚华辉. 准素数阶子群的弱Φ-可补[J]. 理论数学, 2018, 8(4): 345-349. https://doi.org/10.12677/PM.2018.84046

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