A note on Polya groups

Étienne Emmelin

A note on Polya groups

Number Theory 2023-03-10 v2

Authors: Étienne Emmelin

Abstract

Let $K/\mathbf{Q}$ be a finite Galois extension. The P\'olya group of $K$ is the subgroup of the class group $Cl(K)$ , generated by the classes of ambiguous ideals of $K$ . In this note, among other results, we prove that every finite abelian group is isomorphic to the P\'olya group of a number field.

Keywords

galois theory abelian groups abelian varieties

Cite

@article{arxiv.2302.07977,
  title  = {A note on Polya groups},
  author = {Étienne Emmelin},
  journal= {arXiv preprint arXiv:2302.07977},
  year   = {2023}
}

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