Finite supersolvable groups and Hall normally embedded subgroups of prime power order

Zheng, Weicheng1; Meng, Wei1,2

2024-07-01

10.1007/s11587-024-00873-6

RICERCHE DI MATEMATICA   影响因子和分区

0035-5038

1827-3491

Let G be a finite group. A groupGis called a T group if its every subnormal subgroup is normal. A subgroup H of G is called Hall normally embedded in G if His a Hallsub group of H-G, where H-G is the normal closure of H in G. Using the notion of Hallnormally embedded subgroups, we characterize supersolvable groups and solvableT-group. First, we prove that if every cyclic subgroup ofGof order prime or 4 isHall normally embedded in G, then G is supersolvable with a well defined structure.Second, we prove that an A-group G is supersolvable if and only if its Sylow subgroupsare products of cyclic Hall normally embedded subgroups ofG. Final, we show that G is a solvable T-group if and only if everyp-subgroup of Gis Hall normally embeddedinG, for all primes p is an element of pi(G)

Hall normally embedded T-group Supersolvable group Solvable group

SCI

英语

通讯

National Natural Science Foundation of China[12161021] ; Guangxi Natural Science Foundation Program[2021GXNSFAA220117] ; Innovation Project of GUET Graduate Education[2023YCXS112]

Mathematics

Mathematics, Applied ; Mathematics

WOS:001262474100001

SPRINGER-VERLAG ITALIA SRL

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

Zheng, Weicheng,Meng, Wei. Finite supersolvable groups and Hall normally embedded subgroups of prime power order[J]. RICERCHE DI MATEMATICA,2024.

Zheng, Weicheng,&Meng, Wei.(2024).Finite supersolvable groups and Hall normally embedded subgroups of prime power order.RICERCHE DI MATEMATICA.

Zheng, Weicheng,et al."Finite supersolvable groups and Hall normally embedded subgroups of prime power order".RICERCHE DI MATEMATICA (2024).