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

Mathematics

Research output: Contribution to a Journal (Peer & Non Peer) › 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	P1
DOIs	https://doi.org/10.1016/j.jsc.2014.08.011
Publication status	Published - 1 May 2015

Keywords

Algebraic group
Algorithm
Arithmetic group
Lattice

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10.1016/j.jsc.2014.08.011

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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.",

keywords = "Algebraic group, Algorithm, Arithmetic group, Lattice",

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year = "2015",

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doi = "10.1016/j.jsc.2014.08.011",

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AU - Detinko, A. S.

AU - Flannery, D. L.

AU - de Graaf, W. A.

PY - 2015/5/1

Y1 - 2015/5/1

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 - Algebraic group

KW - Algorithm

KW - Arithmetic group

KW - Lattice

UR - https://www.scopus.com/pages/publications/84919351252

U2 - 10.1016/j.jsc.2014.08.011

DO - 10.1016/j.jsc.2014.08.011

M3 - Article

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SP - 138

EP - 145

JO - Journal of Symbolic Computation

JF - Journal of Symbolic Computation

IS - P1

ER -

Integrality and arithmeticity of solvable linear groups

Abstract

Keywords

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