An integral version of a classical embedding theorem concerning quaternion algebras B over a number field k is proved. Assume that B satisfies the Eichler 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# embed into either all or none of the maximal orders of B, it turns out that some #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 maximal arithmetic subgroups of B~*/k~* which contain a given element of B~*/k~* are determined.
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