中文摘要：

已知H是群G的子群，若存在G的子群K，使得G=HK且对于H的任意极大子群Hi都有HiK〈G，其中Hi满足｜H：Hi｜=Pa，则称子群H在G中是Mp-可补的．在群G的Sylow子群的正规化子中，利用某些给定阶子群的Mp-可补性质，结合M-非子群的几乎m嵌入性质，研究有限群的p-幂零性和P-超可解性．

英文摘要：

A subgroupHof Gis called Mp-supplemented in Gif there exists a subgroup K of Gsuch that G= HK and HiK 〈Gfor every maximal subgroupHiof H with｜H：Hi｜=pα.Using the Mp-supplemented properties of some subgroups with fixed order and the nearly m-embedded properties of H-subgroups,some results about p-nilpotency and p-supersolvability of finite groups are obtained.