On finite groups with some Hall normally embedded subgroups

Meng, Wei1,2; Lu, Jiakuan3

2024-02-01

10.1142/S0219498825501907

JOURNAL OF ALGEBRA AND ITS APPLICATIONS   影响因子和分区

0219-4988

1793-6829

Let G be a finite group. A subgroup H of G is called Hall normally embedded in G if H is a Hall subgroup of HG, where HG is the normal closure of H in G, that is, the smallest normal subgroup of G containing H. A group G is called a PHN-group if its all minimal subgroups and cyclic subgroup of order 4 are Hall normally embedded in G. In this paper, we give the classification of minimal non-PHN-groups. Furthermore, we investigate the structure of finite group all of whose maximal subgroups of even order are PHN-groups.

Hall normally embedded minimal subgroup maximal subgroup solvable group

SCI

英语

通讯

National Natural Science Foundation of China[12161021] ; Guangxi Natural Science Foundation Program["2021GXNSFAA220117","2023JJA110108"] ; Innovation Project of Guangxi Graduate Education[XJCY2023018] ; Science and technology project of Guangxi[AD21220114]

Mathematics

Mathematics, Applied ; Mathematics

WOS:001259833800001

WORLD SCIENTIFIC PUBL CO PTE LTD

MATHEMATICS

Web of Science

1.Guilin Univ Elect Technol, Sch Math & Comp Sci, Guilin 541002, Guangxi, Peoples R China
2.Southern Univ Sci & Technol, SUSTech Int Ctr Math, Shenzhen 518055, Guangdong, Peoples R China
3.Guangxi Normal Univ, Sch Math & Stat, Guilin 541004, Guangxi, Peoples R China

Meng, Wei,Lu, Jiakuan. On finite groups with some Hall normally embedded subgroups[J]. JOURNAL OF ALGEBRA AND ITS APPLICATIONS,2024.

Meng, Wei,&Lu, Jiakuan.(2024).On finite groups with some Hall normally embedded subgroups.JOURNAL OF ALGEBRA AND ITS APPLICATIONS.

Meng, Wei,et al."On finite groups with some Hall normally embedded subgroups".JOURNAL OF ALGEBRA AND ITS APPLICATIONS (2024).