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If H and D are two orders in a central simple algebra A with D of maximalrank and containing H, the theory of representation fields describes the set ofspinor genera of orders in the genus of D representing the order H. When H iscontained in a maximal subfield of A and the dimension of A is the square of aprime p, the proportion of spinor genera representing H has the form r/p, infact, when the representation field exists, this proportion is either 1 or 1/p.In the later case the order H is said to be selective for the genus. Thecondition for selectivity is known when D is maximal and also when p = 2 and Dis an Eichler order. In this work we describe the orders H that are selectivefor at least one genus of orders of maximal rank in A.

Maximal selectivity for orders in fields