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.
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.