%0 Journal Article
%A Corrales Rodrigáñez, Carmen
%A Jespers, Eric
%A Leal, Guilherme
%A Rio, Ángel del
%T Presentations of the unit group of an order in a non-split quaternion algebra
%D 2004
%@ 0001-8708
%U https://hdl.handle.net/20.500.14352/49857
%X 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.
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