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

12 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

Access to Document

10.1016/j.jsc.2012.04.002Licence: Other

Cite this

@article{84b8a6e643df42f290986097f2f85f25,

title = "Recognition of finite matrix groups over infinite fields",

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{\textquoteright}s structure. Implementations of our algorithms are available in Magma.",

keywords = "Finitely generated linear group, Finite linear group, Decision problem, Algorithm",

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

year = "2013",

month = mar,

day = "1",

doi = "10.1016/j.jsc.2012.04.002",

language = "English",

volume = "50",

pages = "100–109",

journal = "Journal of Symbolic Computation",

issn = "0747-7171",

publisher = "Academic Press Inc.",

}

TY - JOUR

T1 - Recognition of finite matrix groups over infinite fields

AU - Detinko, Alla

AU - Flannery, Dane

AU - O'Brien, Eamonn

PY - 2013/3/1

Y1 - 2013/3/1

N2 - 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.

AB - 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.

KW - Finitely generated linear group

KW - Finite linear group

KW - Decision problem

KW - Algorithm

UR - https://www.scopus.com/inward/record.uri?eid=2-s2.0-84870254867&doi=10.1016%2fj.jsc.2012.04.002&partnerID=40&md5=801fd185e1b4cabf8d776c4ba453cc93

U2 - 10.1016/j.jsc.2012.04.002

DO - 10.1016/j.jsc.2012.04.002

M3 - Article

VL - 50

SP - 100

EP - 109

JO - Journal of Symbolic Computation

JF - Journal of Symbolic Computation

SN - 0747-7171

ER -

Recognition of finite matrix groups over infinite fields

Abstract

Access to Document

Other files and links

Fingerprint

Cite this