Algorithms for linear groups of finite rank

A. S. Detinko; D. L. Flannery; E. A. O'Brien

doi:10.1016/j.jalgebra.2013.06.006

Algorithms for linear groups of finite rank

A. S. Detinko, D. L. Flannery, E. A. O'Brien

Mathematics

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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
DOIs	https://doi.org/10.1016/j.jalgebra.2013.06.006
Publication status	Published - 1 Nov 2013

Keywords

Algorithm
Linear group
Prüfer rank
Solvable group

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10.1016/j.jalgebra.2013.06.006

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

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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year = "2013",

month = nov,

day = "1",

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

language = "English",

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T1 - Algorithms for linear groups of finite rank

AU - Detinko, A. S.

AU - Flannery, D. L.

AU - O'Brien, E. A.

PY - 2013/11/1

Y1 - 2013/11/1

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 - Algorithm

KW - Linear group

KW - Prüfer rank

KW - Solvable group

UR - https://www.scopus.com/pages/publications/84881549334

U2 - 10.1016/j.jalgebra.2013.06.006

DO - 10.1016/j.jalgebra.2013.06.006

M3 - Article

SN - 0021-8693

VL - 393

SP - 187

EP - 196

JO - Journal of Algebra

JF - Journal of Algebra

ER -

Algorithms for linear groups of finite rank

Abstract

Keywords

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