关键词: 极大子群;半覆盖远离性;极大完备;可解群

Abstract:

The relationships between the semi cover-avoiding property of subgroups  and the solvability of groups are investigated. As an application, some sufficient and necessary conditions for finite groups to be solvable are obtained. It is proved that a finite group G is solvable if and only if for every maximal subgroup M of  G, either M is semi cover-avoiding in G, or M has a solvable m aximal completion C such that C is semi cover-avoiding in G.

Key words: maximal subgroup; semicover-avoiding property; maximal completion; solvable group