海南热带海洋学院学报2025，Vol.32Issue(2)：133-137,5.DOI:10.13307/j.issn.2096-3122.2025.02.14
子群的c-可补充性质对p-幂零群的影响
Influence of c-supplemented Properties of Subgroups on p-nilpotent Subgroups
摘要
Abstract
Let G be a finite group.In order to study the influence of the c-supplemented properties of subgroups of the finite group G on the p-nilpotent groups,starting from the definition of c-supple-mented subgroups,the method of weakening the local conditions was adopted—i.e.,letting P be a Sy-low p-subgroups of G,selecting the primary subgroup H or subgroup K related to P and restricting H or Kp between the commutator subgroup P′ of P and the Frattini subgroup Φ(P)of P.Combined with the conditions that the normalizer NG(P)of subgroup P or the normalizer NG(H)of subgroup H is p-nil-potent,three sufficient conditions on p-nilpotent groups were obtained by using the c-supplemented prop-erties of H or K.Meanwhile,in order to further understand the abstract c-supplemented properties and these three sufficient conditions,a specific example was given for each theorem,respectively.More-over,some corollaries of the theorems of this paper were obtained under three special c-supplemented properties,namely,complementarity,normality and c-normality,respectively.All the results provide an effective reference for investigating the structure of p-nilpotent groups.关键词
c-可补子群/p-幂零群/Sylow子群/准素子群/有限群Key words
c-supplemented subgroups/p-nilpotent subgroups/Sylow subgroups/primary subgroups/fi-nite group分类
数理科学引用本文复制引用
赵佳,张佳..子群的c-可补充性质对p-幂零群的影响[J].海南热带海洋学院学报,2025,32(2):133-137,5.基金项目
国家自然科学基金项目(12371018 （）
12001436) （）
四川省自然科学基金项目(2022NSFSC1843) （2022NSFSC1843）
教育部春晖计划合作科研项目(HZKY20220567) （HZKY20220567）
西华师范大学基本科研业务费项目(17E091 （）
18B032) （）
