有限群的可补子群的相关性质

Some Properties of Complemented Subgroups of Finite Groups

考虑有限群的极小子群和Sylow子群的可补性质对群结构的影响.设F是包含全体有限超可解群的群系,G是有限群,M>1是G的正规子群,且G/M∈F,证明:如果对M的任一极小子群H,H∩F^(*)(G^(F))均在G中可补,则G∈F.

The author considered the influence of the complementability of minimal subgroups and Sylow subgroups on the structure of finite groups.Let F be a formation containing all finite supersolvable groups,and G be a finite group,M>1 be a normal subgroup of G with G/M∈F.The author prove if for any minimal subgroup H of M,H∩F^(*)(G^(F))is complemented in G,then G∈F.