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

作　　者：向艳辉 张佳 XIANG Yan-hui;ZHANG Jia(School of Mathematics and Information,China West Normal University,Nanchong 637009,China)

机构地区：[1]西华师范大学数学与信息学院,四川南充637009

出　　处：《宜春学院学报》2024年第6期8-11,121,共5页Journal of Yichun University

基　　金：国家自然科学基金项目(编号:12001436);教育部春晖计划合作科研项目(编号:HZKY20220567);四川省自然科学基金项目(编号:2022NSFSC1843)。

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ΦH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S_(5),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。A subgroup H of a group G is called an ICΦ-subgroup of G if H∩[H,G]≤Φ(H),whereΦH 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 S_(5).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 S_(5) 超中心 

分 类 号：O152.1[理学—数学]