Corrales Rodrigañez, Carmen and Jespers, Eric and Leal, Guilherme and Rio, Ángel del
(2004)
*Presentations of the unit group of an order in a non-split quaternion algebra.*
Advances in Mathematics, 186
(2).
pp. 498-524.
ISSN 0001-8708

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Official URL: http://www.sciencedirect.com/science/article/pii/S0001870803002585

## Abstract

We give an algorithm to determine a finite set of generators of the unit group of an order in a non-split classical quaternion algebra H(K) over an imaginary quadratic extension K of the rationals. We then apply this method to obtain a presentation for the unit group of H(Z[(1+root-7)/(2)]). As a consequence a presentation is discovered for the orthogonal group SO3(Z[(1+root-7)/(2)]). These results provide the first examples of a characterization of the unit group of some group rings that have an epimorphic image that is an order in a non-commutative division algebra that is not a totally definite quaternion algebra.

Item Type: | Article |
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Uncontrolled Keywords: | Algorithms; Finite sets of generators; Unit groups; Orders; quaternion algebras; Presentations |

Subjects: | Sciences > Mathematics > Group Theory |

ID Code: | 14942 |

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Deposited On: | 20 Apr 2012 11:51 |

Last Modified: | 06 Feb 2014 10:12 |

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