New Criteria for p-Nilpotency of Finite Groups

Abstract

We call a subgroup H of a group G p-nilpotent quotient-supplemented in G if there exists a subgroup K of G such that G = HK and K/K ∩ H _G is p-nilpotent. By using this concept, we establish some new criteria for a group G to be p-nilpotent.

Keywords:

• Finite group
• p-Nilpotent group
• p-Nilpotent quotient-supplemented subgroup
• Sylow subgroup

AMS Classification:

• 20D10
• 20D20

ACKNOWLEDGMENTS

The research of the first and second authors are supported by a research grant of the National Natural Science Foundation of China (Grant # 10471118).

The research of the third author is partially supported by a UGC(Hong Kong) grant # 2160210 (2003/2005) and Tian Yuan Fund of Mathematics of China (Grant # 10626047).

Notes

Communicated by V. A. Artamonov.