Research ArticlesNo Access

$𝔉$ -groups and Hall $s$ -semiembedded subgroups

Yanhui Guo

School of Mathematical Science, Soochow University, Suzhou, Jiangsu 215006, P. R. China

Suzhou University of Science and Technology (Suzhou), Jiangsu 210009, P. R. China

E-mail Address: gyhnju@sohu.com

Corresponding author.

Search for more papers by this author

and

Xianhua Li

School of Mathematical Science, Soochow University, Suzhou, Jiangsu 215006, P. R. China

E-mail Address: xhli@suda.edu.cn

Search for more papers by this author

https://doi.org/10.1142/S0219498817500591Cited by:1 (Source: Crossref)

Abstract

Let $G$ be a finite group. A subgroup $H$ of $G$ is said to be a Hall $s$ -semiembedded subgroup of $G$ if $H$ is a Hall subgroup of $〈 H, P 〉$ for any $P \in {Syl}_{p} (G)$ , where $(p, | H |) = 1$ . In this paper, we investigate the influence of Hall $s$ -semiembedded subgroups on the structure of the finite group $G$ . Some new results about $G$ to be a $𝔉$ -group are obtained, where $𝔉$ is a saturated formation.

Communicated by R. Grigorchuk

Keywords:

AMSC: 20D10, 20D15

References

1. A. Ballester-Bolinches and M. C. Pedraza-Aguilera, On minimal subgroups of finite groups, Acta Math. Hungar. 73(4) (1996) 335–342. Crossref, Web of Science, Google Scholar
2. W. Guo, The Theory of Classes of Groups (Science Press–Kluwer Academic Publishers, 2000). Google Scholar
3. W. Guo, The influence of minimal subgroups on the structure of finite groups, Southeast Asia Bull. Math. 22 (1998) 287–290. Google Scholar
4. B. Huppert, Endliche Gruppen 1 (Springer, New York, 1967). Crossref, Google Scholar
5. B. Huppert and N. Blackburn, Finite Groups III (Springer, Berlin, 1982). Crossref, Google Scholar
6. I. M. Isaacs, Semipermutable $π$ -subgroups, Arch. Math. 102 (2014) 1–6. Crossref, Web of Science, Google Scholar
7. Y. Li, X. He and Y. Wang, On $s$ -semipermutable subgroups of finite groups, Acta Math. Sin. (Engl. Ser.) 26(11) (2010) 2215–2222. Crossref, Web of Science, Google Scholar