Orbit-stabilizer problems and computing normalizers for polycyclic groups

Authors:
Bettina Eick
Affiliations:
Institut für Geometrie, Universität Braunschweig, 38106 Braunschweig, Germany
Venue:
Journal of Symbolic Computation
Year:
2002

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Abstract

We present a practical algorithm to solve the orbit-stabilizer problem for subgroups of the free abelian group Zd under the action of a polycyclic group of automorphisms. As an application we obtain a practical algorithm to compute the normalizer of a subgroup and, similarly, we can solve the subgroup-conjugacy problem in polycyclic groups.