Finite Groups with Π-Supplemented Minimal Subgroups

Abstract

Let H be a subgroup of G. If there is a subgroup T of G such that HT = G and H ∩ T ≤ I ≤ H, where I has Π-property in G, then H is called Π-supplemented in G. By investigating on minimal and 2-minimal subgroups, some criteria of p-nilpotency of finite groups are obtained.

Key Words:

• Finite group
• Minimal subgroups
• p-nilpotent
• Π-supplemented

2000 Mathematics Subject Classification:

• 20D10

ACKNOWLEDGMENT

The author is grateful to the referee for his or her helpful report.

The author was supported by a China Postdoctoral Science Foundation funded project (Grant 20110491726) and a NNSF of P. R. China (Grant 11071229).

Notes

Communicated by V. A. Artamonov.