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+ −7 2 ]) . As a consequence a presentation is discovered for the orthogonal group SO 3( Z[ 1+ −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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