The generators of $3$-class group of some fields of degree $6$ over $\mathbb{Q}$
| العنوان: | The generators of $3$-class group of some fields of degree $6$ over $\mathbb{Q}$ |
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| المؤلفون: | Moulay Chrif Ismaili, Siham Aouissi, Mohamed Talbi, Abdelmalek Azizi |
| المصدر: | Boletim da Sociedade Paranaense de Matemática. 39:37-52 |
| بيانات النشر: | Sociedade Paranaense de Matematica, 2021. |
| سنة النشر: | 2021 |
| مصطلحات موضوعية: | Class (set theory), Mathematics - Number Theory, Degree (graph theory), Group (mathematics), Mathematics::Number Theory, General Mathematics, 010103 numerical & computational mathematics, 11R11, 11R16, 11R20, 11R27, 11R29, 11R37, 01 natural sciences, 010101 applied mathematics, Combinatorics, FOS: Mathematics, Number Theory (math.NT), 0101 mathematics, Mathematics |
| الوصف: | Let $\mathrm{k}=\mathbb{Q}\left(\sqrt[3]{p},\zeta_3\right)$, where $p$ is a prime number such that $p \equiv 1 \pmod 9$, and let $C_{\mathrm{k},3}$ be the $3$-component of the class group of $\mathrm{k}$. In \cite{GERTH3}, Frank Gerth III proves a conjecture made by Calegari and Emerton \cite{Cal-Emer} which gives necessary and sufficient conditions for $C_{\mathrm{k},3}$ to be of $\operatorname{rank}\,$ two. The purpose of the present work is to determine generators of $C_{\mathrm{k},3}$, whenever it is isomorphic to $\mathbb{Z}/9\mathbb{Z} \times \mathbb{Z}/3\mathbb{Z}$. Comment: 16 pages, 2 tables |
| تدمد: | 2175-1188 0037-8712 |
| URL الوصول: | https://explore.openaire.eu/search/publication?articleId=doi_dedup___::fb02bea679d2fe7823c67e11bba5c818 https://doi.org/10.5269/bspm.40672 |
| حقوق: | OPEN |
| رقم الأكسشن: | edsair.doi.dedup.....fb02bea679d2fe7823c67e11bba5c818 |
| قاعدة البيانات: | OpenAIRE |
| تدمد: | 21751188 00378712 |
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