关键词: F-可补子群, p-超可解群, 饱和群系, Fitting子群

Abstract:

We took the advantage of Fsupplemented subgroups to study the structure of p-supersolvable groups and obtained two main results. 1) Let G be p-solvable and p||G|, then G is p-supersolvable if and only if every maximal subgroup of F_p(G) containing O_p′(G) is Fsupplemented in G, where F is the class of all p-supersolvable groups. 2) Let G be p-solvable and p||G|, then G is p-supersolvable if and only if every maximal subgroup of noncyclic Sylow p-subgroups of Fp(G) isFsupplemented in G, where F is the class of all p-supersolvable groups.

Key words: supplemented subgroup, p-supersolvable group, saturated formation, Fitting subgroup