An embedding theorem for quaternion algebras

An integral version of a classical embedding theorem concerning quaternion algebras B over a number held k is proved. Assume that B satisfies the Eich ler condition, that is, some infinite place of k is not ramified in B, and let Omega be an order in a quadratic extension of k. The maximal orders of B which admit an embedding of Omega are determined. Although most Omega emb ed into either all or none of the maximal orders of B, it turns out that so me Omega are 'selective', in the sense that they embed into exactly half of the isomorphism types of maximal orders of B. As an application, the maxim al arithmetic subgroups of B*/k* which contain a given element of B*/k* are determined.