The Pólya group, \(\mathcal {P}_O(K)\) , of a number field K is the subgroup of its ideal class group \(\textrm{C}_K\) generated by the classes of the products of the maximal ideals of K having the same absolute norm. K is said to be a Pólya field if \(\mathcal {P}_O(K)\) is trivial. In this note, we are interested in determining, using capitulation theory, the Pólya groups of some real biquadratic number fields \(K=\mathbb {Q}(\sqrt{d_{1}},\sqrt{d_{2}})\) , where \(d_1\) and \(d_2\) are two square-free positive coprime integers satisfying certain conditions. As a consequence, we deduce all such Pólya fields K, and the structure of their first cohomology group of units.
