Sylow子群的M-可补性对有限群结构的影响

The Influence of M-Supplementation of Sylow Subgroups on the Structure of Finite Groups

对于群G的子群H,若存在G的子群B,使得G=HB,且对H的任意极大子群H1,H1B为G的真子群,则称H在G中是M-可补的.利用群G的Sylow子群在其正规化子中的M-可补性,得到了有关p-幂零性和群系的一些结论.

A subgroup H of G is said to be M-supplemented in G if there exists a subgroup B of G such that G=HB and H1B〈G for every maximal subgroup H1 of H.In this paper,the M-supplementation in NG（P） of G is investigated.Some new results about p-nilpotency and formation are obtained.