Integrality and arithmeticity of solvable linear groups

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

doi:10.1016/j.jsc.2014.08.011

Integrality and arithmeticity of solvable linear groups

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

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

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.

Original language	English
Pages (from-to)	138–145
Number of pages	8
Journal	Journal of Symbolic Computation
Volume	68
Issue number	Part 1
Early online date	11 Aug 2014
DOIs	https://doi.org/10.1016/j.jsc.2014.08.011
Publication status	Published - 1 May 2015
Externally published	Yes

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title = "Integrality and arithmeticity of solvable linear groups",

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. ",

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AU - Flannery, D. L.

AU - Graaf, W. A. de

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N2 - 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.

AB - 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.

KW - Arithmetic group

KW - Algorithm

KW - Algebraic group

KW - Lattice

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DO - 10.1016/j.jsc.2014.08.011

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JO - Journal of Symbolic Computation

JF - Journal of Symbolic Computation

SN - 0747-7171

IS - Part 1

ER -

Integrality and arithmeticity of solvable linear groups

Abstract

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