CAJ | 학술논문

M是有限群G的一个给定极大子群,如果G的子群C不包含在M中,但是C的每个G-不变真子群都被M包含,那么就称C是M的一个完备.如果完备C同时还满足下列条件:或者C=D,或者C是子群D的一个极大子群,其中D不是M的完备,则称C是M的一个S-完备. 利用极大子群的S-完备刻画了有限可解群.
M시유한군G적일개급정겁대자군,여과G적자군C불포함재M중,단시C적매개G-불변진자군도피M포함,나요취칭C시M적일개완비.여과완비C동시환만족하렬조건:혹자C=D,혹자C시자군D적일개겁대자군,기중D불시M적완비,칙칭C시M적일개S-완비. 이용겁대자군적S-완비각화료유한가해군.
For a given maximal subgroup M of a finite group G, a subgroup C of G is said to be a completion of M in G if C is not contained in M while every G-invariant proper subgroup of C is contained in M. An s-completion C of M is a completion satisfying the following condition: either C = G or there exists a subgroup D of G, which is not a completion of M such that D contains C as a maximal subgroup. In this paper, the finite solvable groups are characterized by using s-completions of maximal subgroups.