Computing subgroups by exhibition in finite solvable groups

摘要

We present practical algorithms to compute subgroups such as Hall systems, system normalizers, ξ-normalizers andξ-covering subgroups in finite solvable groups. An appli- cation is an algorithm to calculate head complements in finite solvable groups; that is, complements which are closely related to maximal subgroups. Our algorithms use the technique of exhibiting subgroupd.