Algorithms for linear groups of finite ranks

Alla Detinko; Dane Flannery; Eamonn O'Brien

doi:10.1016/j.jalgebra.2013.06.006

Algorithms for linear groups of finite ranks

Alla Detinko, Dane Flannery, Eamonn O'Brien

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

7 Citations (Scopus)

Abstract

Let G be a finitely generated solvable-by-finite linear group. We present an algorithm to compute the torsion-free rank of G and a bound on the Prüfer rank of G. This yields in turn an algorithm to decide whether a finitely generated subgroup of G has finite index. The algorithms are implemented in Magma for groups over algebraic number fields.

Original language	English
Pages (from-to)	187–196
Number of pages	10
Journal	Journal of Algebra
Volume	393
Issue number	1
Early online date	16 Jul 2013
DOIs	https://doi.org/10.1016/j.jalgebra.2013.06.006
Publication status	Published - 1 Nov 2013
Externally published	Yes

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title = "Algorithms for linear groups of finite ranks",

abstract = "Let G be a finitely generated solvable-by-finite linear group. We present an algorithm to compute the torsion-free rank of G and a bound on the Pr{\"u}fer rank of G. This yields in turn an algorithm to decide whether a finitely generated subgroup of G has finite index. The algorithms are implemented in Magma for groups over algebraic number fields.",

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author = "Alla Detinko and Dane Flannery and Eamonn O'Brien",

year = "2013",

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doi = "10.1016/j.jalgebra.2013.06.006",

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AU - Detinko, Alla

AU - Flannery, Dane

AU - O'Brien, Eamonn

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N2 - Let G be a finitely generated solvable-by-finite linear group. We present an algorithm to compute the torsion-free rank of G and a bound on the Prüfer rank of G. This yields in turn an algorithm to decide whether a finitely generated subgroup of G has finite index. The algorithms are implemented in Magma for groups over algebraic number fields.

AB - Let G be a finitely generated solvable-by-finite linear group. We present an algorithm to compute the torsion-free rank of G and a bound on the Prüfer rank of G. This yields in turn an algorithm to decide whether a finitely generated subgroup of G has finite index. The algorithms are implemented in Magma for groups over algebraic number fields.

KW - Linear group

KW - Solvable group

KW - Algorithm

KW - Prüfer rank

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JO - Journal of Algebra

JF - Journal of Algebra

SN - 0021-8693

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ER -

Algorithms for linear groups of finite ranks

Abstract

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