Invariant part of class group and distribution of relative class group

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Bibliographic Details
Main Author:	Wang, Weitong
Format:	Preprint
Published:	2024
Subjects:	Number Theory
Online Access:	Acceder al recurso
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_version_	1866917074319704064
author	Wang, Weitong
author_facet	Wang, Weitong
contents	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.
format	Preprint
id	arxiv_https___arxiv_org_abs_2408_06676
institution	arXiv
publishDate	2024
record_format	arxiv
spellingShingle	Invariant part of class group and distribution of relative class group Wang, Weitong Number Theory 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.
title	Invariant part of class group and distribution of relative class group
topic	Number Theory
url	https://arxiv.org/abs/2408.06676

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