Invariant part of class group and distribution of relative class group
Number Theory
2025-11-13 v2
Abstract
We generalize the work of Roquette and Zassenhaus on the invariant part of the class groups to the relative class groups. Thereby, we can show some statistical results as follows. For abelian extensions over a fixed number field K, we show infinite Cp-moments for the Sylow p-subgroup of the relative class group when p divides the degree of the extension. For sextic number fields with A4-closure, we can show infinite C2-moments for the Sylow 2-subgroup of the relative class group when the extensions run over a fixed Galois cubic field.
Cite
@article{arxiv.2408.06676,
title = {Invariant part of class group and distribution of relative class group},
author = {Weitong Wang},
journal= {arXiv preprint arXiv:2408.06676},
year = {2025}
}
Comments
The arxiv version is updated so that it is consistent with the published version. It also includes the content of the corrigendum to the published version