Biquadratic Pólya fields with only one quadratic Pólya subfield

A number field is called a Pólya field if the module of integer-valued polynomials over its integers has a regular basis. In this paper, we answer two open questions raised in [4] on biquadratic Pólya fields using some results of [8] and [2] on Galois cohomology of number fields. In particular, we find infinitely many biquadratic Pólya fields with only one quadratic Pólya subfield.