Let K be a number field and denote by 𝒪 K its ring of integers. Let G be a finite group and let K h be a Galois K-algebra with group G. If K h /K is tame, then its ring of integers 𝒪 h is a locally free 𝒪 K G-module by a classical theorem of E. Noether and it defines a class in the locally free class group Cl(𝒪 K G) of 𝒪 K G. We denote by R(𝒪 K G) the set of all such classes. By combining the work of L.R. McCulloh and J. Brinkhuis, we shall prove that the structure of R(𝒪 K G) is connected to the study of embedding problems when G is abelian.