Corrales Rodrigáñez, Carmen2023-06-202023-06-202012ISSN 1096-165810.1016/j.jnt.2011.12.009https://hdl.handle.net/20.500.14352/43683Unit groups of orders in quaternion algebras over number fields provide important examples of non-commutative arithmetic groups. Let K = Q(d ) be a quadratic field with d < 0 a squarefree integer such that d ≡ 1(mod 8), and let R be its ring of integers. In this note we study, through its representation in SO3(R), the group of units of several orders in the quaternion algebra over K with basis {1, i, j,k} satisfying the relations i2 =j2 =−1, i j =−ji =k.engjournal articlehttp://www.sciencedirect.com/science/article/pii/S0022314X12000078http://www.sciencedirect.comrestricted access511Quaternion algebrasQuadratic fieldsSpecial orthogonal group of the space of pure quaternions in a quaternion algebra over a quadratic fieldTeoría de números1205 Teoría de Números