Abstract: For a maximal subgroup M of a group G,a θ-completion for M is a subgroup C such that C is not contained in M while Ma,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 θ-completions and obtain some new results.

Key words:

θ-completion,  , normal , index,  , solvability