中文摘要：

如果存在群G的子群B满足G=HB，并且TB〈G，其中T是H中包含HG的任意极大子群，HG是包含在H中G的最大的正规子群，那么子群H称为在群G中弱μ-可补．利用子群的弱μ-可补性对群的结构进行研究，得到有关群的P-幂零性和P-超可解性的一些新结果．

英文摘要：

A subgroup H of a group G is said to be weakly m-supplemented in G if there exists a subgroup B of G such that G=HB, and TB〈G for any maximal subgroup T of H with HG≤T, where Ha is the largest normal subgroup of G contained in H. In this paper, the influence of weakly m-supplemented subgroup on the structure of finite group is investigated and some conditions for p-nilpotent and p-supersolvable of finite group are obtained.