Finite group with Hall normally embedded minimal subgroups

Cui，Liang1; Zheng，Weicheng1; Meng，Wei1,2; Lu，Jiakuan3

2023

10.1080/00927872.2023.2204964

Communications in Algebra   Impact Factor & Quartile

0092-7872

1532-4125

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 H (Formula presented.), where H (Formula presented.) is the normal closure of H in G, that is, the smallest normal subgroup of G containing H. A group G is called an HNE -group if all cyclic subgroups of order 2 and 4 of G are Hall normally embedded in G. In this paper, we prove that all HNE -groups are 2-nilpotent. Furthermore, we also characterize the structure of finite group all of whose maximal subgroups are HNE -groups. Finally, we determine finite non-solvable groups all of whose second maximal subgroups are HNE -groups.

2-nilpotent group Hall normally embedded second maximal subgroup

SCI

English

Corresponding

WOS:000980177400001

MATHEMATICS

2-s2.0-85158893029

Scopus

1.School of Mathematics and Computing Science,Guilin University of Electronic Technology,Guilin,Guangxi,China
2.SUSTech International Center for Mathematics,Shenzhen,Guangdong,China
3.School of Mathematics and Statistics,Guangxi Normal University,Guilin,Guangxi,China

Cui，Liang,Zheng，Weicheng,Meng，Wei,et al. Finite group with Hall normally embedded minimal subgroups[J]. Communications in Algebra,2023.

Cui，Liang,Zheng，Weicheng,Meng，Wei,&Lu，Jiakuan.(2023).Finite group with Hall normally embedded minimal subgroups.Communications in Algebra.

Cui，Liang,et al."Finite group with Hall normally embedded minimal subgroups".Communications in Algebra (2023).