$5$-rank of ambiguous class groups of quintic Kummer extensions
| Autor: | Elmouhib, Fouad, Talbi, Mohamed, Azizi, Abdelmalek |
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| Rok vydání: | 2020 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1007/s12044-022-00660-z |
| Popis: | Let $k \,=\, \mathbb{Q}(\sqrt[5]{n},\zeta_5)$, where $n$ is a positive integer, $5^{th}$ power-free, whose $5-$class group is isomorphic to $\mathbb{Z}/5\mathbb{Z}\times\mathbb{Z}/5\mathbb{Z}$. Let $k_0\,=\,\mathbb{Q}(\zeta_5)$ be the cyclotomic field containing a primitive $5^{th}$ root of unity $\zeta_5$. Let $C_{k,5}^{(\sigma)}$ the group of the ambiguous classes under the action of $Gal(k/k_0)$ = $<\sigma>$. The aim of this paper is to determine all integers $n$ such that the group of ambiguous classes $C_{k,5}^{(\sigma)}$ has rank $1$ or $2$. Comment: 18 pages, 1 figure |
| Databáze: | arXiv |
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