A Brief Survey of Recent Results on Pólya Groups

The Pólya group of a number field is a particular subgroup of the ideal class group of that number field. In this article, we discuss some recent results on Pólya groups of number fields, their connection with the ring of integer-valued polynomials, and touches upon some results on number fields having large Pólya groups. We include the proof of Zantema’s theorem which laid the foundation to determine the Pólya groups of many finite Galois extensions over \(\mathbb {Q}\) . At the end, we provide an elementary proof of a weaker version of a recent result of Cherubini et al.