设G是有限群,M是G的极大子群.令K/N是G的一个主因子,K≤M而N(2=M,称MnN/K为M的一个CI-截,M的所有CI-截都同构.M在G中的一个完备是G的一个子群C,如果C(z=M,而C的每个G不变真子群都在M中.应用这些概念,本文得到了有关有限群可解性的新结论.
Let G be a finite group and let M be a maximal subgroup of G. For a G-chief factor K/ N satisfying N≤M but K M, we call MNK/N a c-section of M. All c-sections of M are iso- morphic. A completion of M in G is a subgroup C of G such that C M while every proper sub- group of C which is normal in G is contained in M. By means of these concepts,some new re- sults on the solvability of finite groups are obtained.