On ℱ_s-Quasinormal Subgroups of Finite Groups

Abstract

Let G be a finite group and ℱ a formation of finite groups. We say that a subgroup H of G is ℱ _s -quasinormal in G if there exists a normal subgroup T of G such that HT is s-permutable in G and (H ∩ T)H _G /H _G is contained in the ℱ-hypercenter of G/H _G . In this article, we use ℱ _s -quasinormal subgroups to study the structure of finite groups. A series of known results are generalized.

Key Words:

• Finite groups
• Maximal subgroups
• Minimal subgroups
• ℱ _s -Quasinormal subgroups
• Saturated formation

2000 Mathematics Subject Classification:

• 20D10
• 20D15
• 20D20

ACKNOWLEDGMENTS

The author would like to thank the referee for his valuable suggestions which helped to improve the presentation of this article.

Research is supported by NNSF Grant of China (grant: 10771180).

Notes

Communicated by V. A. Artamonov.