Testing polycyclicity of finitely generated rational matrix groups

Assmann, Björn; Eick, Bettina

doi:10.1090/S0025-5718-07-01979-5

Testing polycyclicity of finitely generated rational matrix groups
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by Björn Assmann and Bettina Eick;

Math. Comp. 76 (2007), 1669-1682

DOI: https://doi.org/10.1090/S0025-5718-07-01979-5

Published electronically: March 9, 2007

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Abstract:

We describe algorithms for testing polycyclicity and nilpotency for finitely generated subgroups of $\mathrm {GL}(d,\mathbb {Q})$ and thus we show that these properties are decidable. Variations of our algorithm can be used for testing virtual polycyclicity and virtual nilpotency for finitely generated subgroups of $\mathrm {GL}(d,\mathbb {Q})$.

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