On SSH-subgroups and the structure of finite groups

被引：0

作者：

Wei, Huaquan ^{[1
]}

Sun, Changman ^{[1
]}

Wu, Hui ^{[1
]}

Chen, Yi ^{[1
]}

Zhang, Jiamin ^{[1
]}

机构：

[1] Guangxi Univ, Coll Math & Informat Sci, Nanning 530004, Peoples R China

来源：

JOURNAL OF ALGEBRA AND ITS APPLICATIONS | 2024年

关键词：

s-permutable; SSH-subgroup; maximal subgroup; p-nilpotent; MINIMAL SUBGROUPS; QUASINORMALITY; NORMALITY;

D O I：

10.1142/S0219498825503451

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A subgroup H of a group G is called an SSH-subgroup in G if there exists an s-permutable subgroup K of G such that H-sG = HK and H-g boolean AND N-K(H) <= H for all g is an element of G, where H-sG is the intersection of all s-permutable subgroup of G containing H. In this paper, we present two new sufficient and necessary conditions on the p-nilpotency of finite groups by use of a small quantity of SSH-subgroups of Sylow p-subgroups. A number of known results are improved and extended.

引用

页数：10

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