Corrales Rodrigáñez, CarmenJespers, EricLeal, GuilhermeRio, Ángel del2023-06-202023-06-2020040001-870810.1016/j.aim.2003.07.015https://hdl.handle.net/20.500.14352/49857We 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.engjournal articlehttp://www.sciencedirect.com/science/article/pii/S0001870803002585http://www.sciencedirect.com/restricted access512.54AlgorithmsFinite sets of generatorsUnit groupsOrdersquaternion algebrasPresentationsGrupos (Matemáticas)