Quaternion orders with good divisibility

We examine quaternion orders with the complete factorization property. It is proved that all the indefinite quaternion orders have this property and that there is only a finite number of nonisomorphic definite quaternion orders with this property. The relation of this property to the properties of spinor genera of norm forms is established.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 151, pp. 78–94, 1986.