几类特殊极大子群的极大完备与有限群可解性

Maximal Completions and Solvability of Two Special Maximal Subgroups of Finite Groups

有限群的可解性是有限群论研究的一个主要方向,在可解群的研究中,有限群的极大子群在群论的研究中一直扮演着重要的角色.赋于极大子群若干条件,研究其对有限群本身的结构的影响,这是长期以来令人感兴趣的课题.尝试在小范围F2(G)和Fod(G)中的极大子群附加上一些条件,来研究有限群的可解性的充分必要条件.

Solvability of finite groups is a main direction of research in the study of solvable groups.Adding some conditions to maximal subgroups,to study their impact on the structure of finite groups is a long-standing topic of interest.In this paper,we attempt to establish some necessary and sufficient conditions of finite solvable groups in F2（G） and Fod（G）.