关于ICΦ-子群和p-超可解超中心的结果
Some Results on ICΦ-subgroups and p-supersolvable Hypercenter
向艳辉 1张佳1
作者信息
- 1. 西华师范大学 数学与信息学院,四川 南充 637009
- 折叠
摘要
设H是群G的子群.如果H ∩[H,G]≤Φ(H),则称H是G的ICΦ-子群,这里Φ(H)是H的Frattini子群.围绕此概念,首先,对于奇素数,基于Kaspczyk的p-幂零结果,分析了给定阶子群的ICΦ-性质对p-超可解超中心结构的影响;其次,对于5次对称群S5,确定了ICΦ-子群的所有类型.这些结果为子群的ICΦ-性质的研究提供了具体的例子,也为丰富该课题的研究做出了积极的尝试.
Abstract
A subgroup H of a group G is called an ICΦ-subgroup of G if H ∩[H,G]≤Φ(H),where Φ(H)is the Frattini subgroup of H.Based on this concept,firstly,for odd prime numbers,by the p-nilpotent result of Kaspczyk,we analyzed the influence of the ICΦ-properties of subgroups with a given order on the structure of p-supersolvable hypercenter.Secondly,we determined the types of all ICΦ-subgroups in the symmetric group S5.These results will provide specific examples for the study of ICΦ-properties of subgroups,and also make positive attempts to enrich the research of this topic.
关键词
ICΦ-子群/Frattini子群/S5/超中心Key words
ICΦ-subgroup/Frattini subgroups/S5/hypercenter引用本文复制引用
出版年
2024
NETL
NSTL
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