UBC Number Theory Seminar: Abbas Maarefparvar

For a number field K, the P\'olya group of K, denoted by Po(K), is the subgroup of the ideal class group of K generated by the classes of the products of maximal ideals of K with the same norm. In this talk, after reviewing some results concerning Po(K), I will generalize this notion to the relative P\'olya group Po(K/F), for K/F a finite extension of number fields. Accordingly, I will generalize some results in the literature about P\'olya groups to the relative case. Then, due to some essential observations, I will explain why we need to modify the notion of the relative P\'olya group to the Ostrowski quotient Ost(K/F) to get a more 'accurate' generalization of Po(K). The talk is based on a joint work with Ali Rajaei (Tarbiat Modares University) and Ehsan Shahoseini (Institute For Research In Fundamental Sciences).