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Integrality and arithmeticity of solvable linear groups

Detinko, A.S.; Flannery, D.L.; de Graaf, W.A.

Authors

A.S. Detinko

D.L. Flannery

W.A. de Graaf



Abstract

We develop a practical algorithm to decide whether a finitely generated subgroup of a solvable algebraic group G is arithmetic. This incorporates a procedure to compute a generating set of an arithmetic subgroup of G. We also provide a simple new algorithm for integrality testing of finitely generated solvable-by-finite linear groups over the rational field. The algorithms have been implemented in Magma.

Journal Article Type Article
Publication Date 2015-05
Journal Journal of Symbolic Computation
Print ISSN 0747-7171
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 68
Issue Part 1
Pages 138-145
APA6 Citation Detinko, A., Flannery, D., & de Graaf, W. (2015). Integrality and arithmeticity of solvable linear groups. Journal of Symbolic Computation, 68(Part 1), 138-145. https://doi.org/10.1016/j.jsc.2014.08.011
DOI https://doi.org/10.1016/j.jsc.2014.08.011
Keywords Algebra and Number Theory; Computational Mathematics
Publisher URL https://www.sciencedirect.com/science/article/pii/S0747717114000613?via%3Dihub
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