For a maximal subgroup M of a group G, a g-completion for M is a subgroup C such that C is not contained in M while MG, the core of M in G, is contained in C and C/MG has no proper normal subgroup of G/MG. This concep...For a maximal subgroup M of a group G, a g-completion for M is a subgroup C such that C is not contained in M while MG, the core of M in G, is contained in C and C/MG has no proper normal subgroup of G/MG. This concept was introduced by ZHAO Yao-qing in 1998. In this paper we characterize the solvability of finite groups by means of g-completions and obtain some new results.展开更多
文摘For a maximal subgroup M of a group G, a g-completion for M is a subgroup C such that C is not contained in M while MG, the core of M in G, is contained in C and C/MG has no proper normal subgroup of G/MG. This concept was introduced by ZHAO Yao-qing in 1998. In this paper we characterize the solvability of finite groups by means of g-completions and obtain some new results.
