On SS-Quasinormal Subgroups of Finite Groups

Abstract

A subgroup of a group G is said to be Sylow-quasinormal (S-quasinormal) in G if it permutes with every Sylow subgroup of G. A subgroup H of a group G is said to be Supplement-Sylow-quasinormal (SS-quasinormal) in G if there is a supplement B of H to G such that H is permutable with every Sylow subgroup of B. In this article, we investigate the influence of SS-quasinormal of maximal or minimal subgroups of Sylow subgroups of the generalized Fitting subgroup of a finite group.

Key Words:

• Nilpotent groups
• p-nilpotent groups
• Saturated formations
• S-quasinormal subgroups
• SS-quasinormal subgroups
• Supersolvable groups

2000 Mathematics Subject Classification:

• 20D10
• 20D20

ACKNOWLEDGMENTS

The authors are grateful to the referee and the editor, Prof. M. R. Dixon, who provided their helpful comments and detailed report. The project is supported in part by the Natural Science Foundation of China (No. 10161001), the Natural Science Foundation of Guangxi autonomous region (No. 0249001), and the Innovation Project of Guangxi Graduate Education (No. 2007105930701M30).

Notes

Communicated by M. R. Dixon.