CAJ | 학술논문

利用F-可补子群研究p-超可解群，得到了两个主要结果：1)令G是p-可解的且p||G|，则G是p-超可解的当且仅当Fp(G)中包含Op′(G)的所有极大子群在G中F-可补，这里F是所有p-超可解群组成的群类；2)令G是p-可解的且p||G|，则G是p-超可解的当且仅当Fp(G)的非循环Sylowp-子群的极大子群在G中F-可补，这里F是包含所有p-超可解群组成的群类。
이용F-가보자군연구p-초가해군，득도료량개주요결과：1)령G시p-가해적차p||G|，칙G시p-초가해적당차부당Fp(G)중포함Op′(G)적소유겁대자군재G중F-가보，저리F시소유p-초가해군조성적군류；2)령G시p-가해적차p||G|，칙G시p-초가해적당차부당Fp(G)적비순배Sylowp-자군적겁대자군재G중F-가보，저리F시포함소유p-초가해군조성적군류。
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 Fp (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 Fp (G)is F-supplemented in G,where F is the class of all p-supersolvable groups.