The paper Computing subgroups by exhibition in finite solvable groups by Bettina Eick and Charles R.B. Wright describes practical algorithms to compute subgroups such as Sylow systems, system normalizers, F-normalizers and F-covering groups in finite solvable groups. An application is an algorithm to calculate head complements in such groups. The algorithms, which do not rely on chief factors, modify polycyclic generating sequences to exhibit the desired subgroups. For commonly considered formations, the algorithms run in time polynomial in the composition length of the group and the largest prime divisor of its order.
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Last modified 9-11-01 by CRBW