Algorithms for the Tits alternative and related problems

Alla Detinko; Dane Flannery; Eamonn O'Brien

doi:10.1016/j.jalgebra.2011.06.036

Algorithms for the Tits alternative and related problems

Alla Detinko, Dane Flannery, Eamonn O'Brien

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

14 Citations (Scopus)

Abstract

We present an algorithm to decide whether a finitely generated linear group over an infinite field is solvable-by-finite, thereby obtaining a computationally effective version of the Tits alternative. We also give algorithms to decide whether the group is nilpotentby-finite, abelian-by-finite, or central-by-finite. Implementations of the algorithms are publicly available in Magma.

Original language	English
Pages (from-to)	397-406
Number of pages	10
Journal	Journal of Algebra
Volume	344
Issue number	1
Early online date	12 Aug 2011
DOIs	https://doi.org/10.1016/j.jalgebra.2011.06.036
Publication status	Published - 15 Oct 2011
Externally published	Yes

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Cite this

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abstract = "We present an algorithm to decide whether a finitely generated linear group over an infinite field is solvable-by-finite, thereby obtaining a computationally effective version of the Tits alternative. We also give algorithms to decide whether the group is nilpotentby-finite, abelian-by-finite, or central-by-finite. Implementations of the algorithms are publicly available in Magma.",

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AB - We present an algorithm to decide whether a finitely generated linear group over an infinite field is solvable-by-finite, thereby obtaining a computationally effective version of the Tits alternative. We also give algorithms to decide whether the group is nilpotentby-finite, abelian-by-finite, or central-by-finite. Implementations of the algorithms are publicly available in Magma.

KW - Finitely generated linear group

KW - Solvable-by-finite group

KW - Decision problems

KW - Algorithm

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DO - 10.1016/j.jalgebra.2011.06.036

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Algorithms for the Tits alternative and related problems

Abstract

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