Recognition of finite matrix groups over infinite fields

Alla Detinko; Dane Flannery; Eamonn O'Brien

doi:10.1016/j.jsc.2012.04.002

Recognition of finite matrix groups over infinite fields

Alla Detinko, Dane Flannery, Eamonn O'Brien

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

10 Citations (Scopus)

Abstract

We present a uniform methodology for computing with finitely generated matrix groups over any infinite field. As one application, we completely solve the problem of deciding finiteness in this class of groups. We also present an algorithm that, given such a finite group as input, in practice successfully constructs an isomorphic copy over a finite field, and uses this copy to investigate the group’s structure. Implementations of our algorithms are available in Magma.

Original language	English
Pages (from-to)	100–109
Number of pages	10
Journal	Journal of Symbolic Computation
Volume	50
Early online date	14 Jun 2012
DOIs	https://doi.org/10.1016/j.jsc.2012.04.002
Publication status	Published - 1 Mar 2013
Externally published	Yes

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KW - Decision problem

KW - Algorithm

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Recognition of finite matrix groups over infinite fields

Abstract

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