On Weakly ss-Supplemented Subgroups of Finite Groups

Authors

  • Guo Zhong School of Information Science and Technology, Guangdong University of Foreign Studies, China
  • Shixun Lin School of Mathematics and Statistics, Zhaotong University, China
  • Yan Han School of Mathematics and Statistics, Zhaotong University, China
  • Guoqiong Zhou School of Mathematics and Statistics, Zhaotong University, China

DOI:

https://doi.org/10.7546/CRABS.2022.12.02

Keywords:

weakly ss-supplemented subgroups, nilpotentcy, supersolvability, saturated formation

Abstract

Let H be a subgroup of a finite group G. We say that H is weakly ss-supplemented in G if there exists a subgroup T of G and an s-semipermutable subgroup Hss of G contained in H such that G = HT and HTHss. In this paper, we get some new characterizations of supersolvability and nilpotentcy of G by assuming some minimal subgroups of G are weakly ss-supplemented. Some recent results are extended and generalized.

Author Biographies

Guo Zhong, School of Information Science and Technology, Guangdong University of Foreign Studies, China

Mailing Address:
School of Information Science
and Technology,
Guangdong University of Foreign Studies,
Guangzhou
510000, P. R. China

E-mail: guozhong@um.edu.mo

Shixun Lin, School of Mathematics and Statistics, Zhaotong University, China

Mailing Address:
School of Mathematics and Statistics,
Zhaotong University
Zhaotong 657000, P. R. China

E-mail: shixunlin@163.com

Yan Han, School of Mathematics and Statistics, Zhaotong University, China

Mailing Address:
School of Mathematics and Statistics,
Zhaotong University
Zhaotong 657000, P. R. China

E-mail: hanyan702@126.com

Guoqiong Zhou, School of Mathematics and Statistics, Zhaotong University, China

Mailing Address:
School of Mathematics and Statistics,
Zhaotong University
Zhaotong 657000, P. R. China

E-mail: guoqiongzhou@yeah.net

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Published

23-12-2022

How to Cite

[1]
G. Zhong, S. Lin, Y. Han, and G. Zhou, “On Weakly ss-Supplemented Subgroups of Finite Groups”, C. R. Acad. Bulg. Sci., vol. 75, no. 12, pp. 1715–1724, Dec. 2022.

Issue

Section

Mathematics