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On the orbit-stabilizer problem for integral matrix actions of polycyclic groups

Authors: Bettina Eick and Gretchen Ostheimer
Journal: Math. Comp. 72 (2003), 1511-1529
MSC (2000): Primary 20F16, 20-04; Secondary 68W30
Published electronically: February 3, 2003
MathSciNet review: 1972750
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Abstract | References | Similar Articles | Additional Information

Abstract: We present an algorithm to solve the orbit-stabilizer problem for a polycyclic group $G$ acting as a subgroup of $GL(d, \mathbb Z)$ on the elements of $\mathbb Q^d$. We report on an implementation of our method and use this to observe that the algorithm is practical.

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Additional Information

Bettina Eick
Affiliation: Institut für Geometrie, Universität Braunschweig, 38106 Braunschweig, Germany

Gretchen Ostheimer
Affiliation: Department of Computer Science, 103 Hofstra University, Hempstead, New York 11549

Received by editor(s): July 9, 2001
Published electronically: February 3, 2003
Additional Notes: The authors thank Werner Nickel for useful discussions.
Article copyright: © Copyright 2003 American Mathematical Society

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