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. © 2014 Elsevier Ltd. All rights reserved.

Integrality and arithmeticity of solvable linear groups / Detinko, A. S.; Flannery, D. L.; De Graaf, Willem Adriaan. - In: JOURNAL OF SYMBOLIC COMPUTATION. - ISSN 0747-7171. - 68:1(2015), pp. 138-145. [10.1016/j.jsc.2014.08.011]

Integrality and arithmeticity of solvable linear groups

De Graaf, Willem Adriaan
2015-01-01

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. © 2014 Elsevier Ltd. All rights reserved.
2015
1
Detinko, A. S.; Flannery, D. L.; De Graaf, Willem Adriaan
Integrality and arithmeticity of solvable linear groups / Detinko, A. S.; Flannery, D. L.; De Graaf, Willem Adriaan. - In: JOURNAL OF SYMBOLIC COMPUTATION. - ISSN 0747-7171. - 68:1(2015), pp. 138-145. [10.1016/j.jsc.2014.08.011]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11572/138665
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