Algorithms for computing with nilpotent matrix groups over infinite domains

A. S. Detinko; D. L. Flannery

doi:10.1016/j.jsc.2007.08.001

Algorithms for computing with nilpotent matrix groups over infinite domains

A. S. Detinko, D. L. Flannery

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

8 Citations (Scopus)

Abstract

We develop methods for computing with matrix groups defined over a range of infinite domains, and apply those methods to the design of algorithms for nilpotent groups. In particular, we provide a practical nilpotency testing algorithm for matrix groups over an infinite field. We also provide algorithms to answer a number of structural questions for a nilpotent matrix group.The main algorithms have been implemented in GAP, for groups over the rational number field.

Original language	English
Pages (from-to)	8-26
Number of pages	19
Journal	Journal of Symbolic Computation
Volume	43
Issue number	1
Early online date	17 Aug 2007
DOIs	https://doi.org/10.1016/j.jsc.2007.08.001
Publication status	Published - 1 Jan 2008
Externally published	Yes

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title = "Algorithms for computing with nilpotent matrix groups over infinite domains",

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keywords = "Infinite field, Matrix group, Nilpotency testing, Nilpotent group",

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note = "Funding Information: This publication has emanated from research conducted with the financial support of Science Foundation Ireland. The first author was supported by Deutscher Akademischer aus Tauschdienst (DAAD) grant A/06/32418. Copyright: Copyright 2007 Elsevier B.V., All rights reserved.",

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AU - Flannery, D. L.

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N2 - We develop methods for computing with matrix groups defined over a range of infinite domains, and apply those methods to the design of algorithms for nilpotent groups. In particular, we provide a practical nilpotency testing algorithm for matrix groups over an infinite field. We also provide algorithms to answer a number of structural questions for a nilpotent matrix group.The main algorithms have been implemented in GAP, for groups over the rational number field.

AB - We develop methods for computing with matrix groups defined over a range of infinite domains, and apply those methods to the design of algorithms for nilpotent groups. In particular, we provide a practical nilpotency testing algorithm for matrix groups over an infinite field. We also provide algorithms to answer a number of structural questions for a nilpotent matrix group.The main algorithms have been implemented in GAP, for groups over the rational number field.

KW - Infinite field

KW - Matrix group

KW - Nilpotency testing

KW - Nilpotent group

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ER -

Algorithms for computing with nilpotent matrix groups over infinite domains

Abstract

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