On ℳ_p-Supplemented Subgroups of Finite Groups

Abstract

A subgroup H of G is called ℳ _p -supplemented in G if there exists a subgroup B of G such that G = HB and TB < G for every maximal subgroup T of H with |H: T| =p ^α. In this paper, we investigate the influence of ℳ _p -supplemented subgroup and some conditions for p-nilpotency and p-supersolvability of finite groups are obtained.

Key Words:

• Finite groups
• p-supersolvable
• p-nilpotent
• ℳ _p -supplemented
• Sylow subgroups

2010 AMS Subject Classification:

• 20D10
• 20D20

ACKNOWLEDGMENT

We thank the referee for his/her careful reading of the manuscript and for his/her suggestions which have helped to improve our original version.

This research is supported by the grant of NSFC (Grants #11271016 and #10901133) and sponsored by Natural science fund for colleges and universities in Jiangsu Province.

Notes

Communicated by V. A. Artamonov.