On P\'olya groups of some non-Galois number fields

We prove two conjectures proposed by Chabert and Halberstadt concerning P\'olya groups of S₄-fields and D₄-fields. More generally, the latter will be proved for Dₙ-fields with n 4 an even integer. Further, generalizing a result of Zantema, we also prove that the pre-P\'olya group of a non-Galois field of a prime degree, e. g. an A₅-field, coincides with its P\'olya group.