Pólya groups and fields in some real biquadratic number fields

Let K be a number field and O_K be its ring of integers. Let Π_q (K) be the product of all prime ideals of O_K with absolute norm q. The Pólya group of a number field K is the subgroup of the class group of K generated by the classes of Π_q (K). K is a Pólya field if and only if the ideals Π_q (K) are principal. In this paper, we follow the work that we have done in [S. EL Madrari, “On the Pólya fields of some real biquadratic fields”, Matematicki Vesnik, online 05.09.2024] where we studied the Pólya groups and fields in a particulare cases. Here, we will give the Pólya groups of K=Q(√(d_1 ),√(d_2 )) such that d_1=lm_1 and d_2=lm_2 are square-free integers with l>1 and gcd(m_1;m_2)=1 and the prime 2 is not totally ramified in K⁄Q. And then, we characterize the Pólya fields of the real biquadratic fields K.