The Influence Of (?)-Supplemented Properties Of Subgroups On The Structure Of Finite Groups

In this paper, we study the influence of F-supplemented properties of subgroups on thestructure of solvable groups and p-groups. The main results are cited as following:Theorem3.1.1Let G be a finite group, G is solvable if and only if for every maximalsubgroup P₁of any Sylow2-subgroup P of G, P1is S-supplemented in G.Theorem3.2.1Let P be a Sylow p-subgroup of finite group G, where p is a primedivisor of the order of G,（|G|,p-1）=1. Then G is p-nipotent if and only if every maximalsubgroup of P is N-supplemented in G.