Integrality and arithmeticity of solvable linear groups

05/10/2019

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by   W. A. de Graaf, et al.

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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.