Unramified extensions of some cyclic quartic fields
In this paper we determine the fourteen unramified extensions for some cyclic quartic fields $K$ whose $2$-class group $C_{K,2}$ is isomorphic to ${\mathbb{Z}}/{2{\mathbb{Z}}}\times {\mathbb{Z}}/{2{\mathbb{Z}}} \times {\mathbb{Z}}/{2{\mathbb{Z}}}$ and to characterize the generators of $C_{K,2}$.
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Sociedade Brasileira de Matemática
2018-01-01
|
| Series: | Boletim da Sociedade Paranaense de Matemática |
| Subjects: | |
| Online Access: | http://periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/31299 |
| _version_ | 1819265048773656576 |
|---|---|
| author | Mohammed Talbi Abdelmalek Azizi Idriss Jerrari |
| author_facet | Mohammed Talbi Abdelmalek Azizi Idriss Jerrari |
| author_sort | Mohammed Talbi |
| collection | DOAJ |
| description | In this paper we determine the fourteen unramified extensions for some cyclic quartic fields $K$ whose $2$-class group $C_{K,2}$ is isomorphic to ${\mathbb{Z}}/{2{\mathbb{Z}}}\times {\mathbb{Z}}/{2{\mathbb{Z}}} \times {\mathbb{Z}}/{2{\mathbb{Z}}}$ and to characterize the generators of $C_{K,2}$. |
| first_indexed | 2024-12-23T20:39:11Z |
| format | Article |
| id | doaj.art-72fa3345367940ef82db7ecbc5343833 |
| institution | Directory Open Access Journal |
| issn | 0037-8712 2175-1188 |
| language | English |
| last_indexed | 2024-12-23T20:39:11Z |
| publishDate | 2018-01-01 |
| publisher | Sociedade Brasileira de Matemática |
| record_format | Article |
| series | Boletim da Sociedade Paranaense de Matemática |
| spelling | doaj.art-72fa3345367940ef82db7ecbc53438332022-12-21T17:31:59ZengSociedade Brasileira de MatemáticaBoletim da Sociedade Paranaense de Matemática0037-87122175-11882018-01-0136121522110.5269/bspm.v36i1.3129915360Unramified extensions of some cyclic quartic fieldsMohammed Talbi0Abdelmalek Azizi1Idriss Jerrari2Mohamed First UniversityMohamed First UniversityRegional center of Education and TrainingIn this paper we determine the fourteen unramified extensions for some cyclic quartic fields $K$ whose $2$-class group $C_{K,2}$ is isomorphic to ${\mathbb{Z}}/{2{\mathbb{Z}}}\times {\mathbb{Z}}/{2{\mathbb{Z}}} \times {\mathbb{Z}}/{2{\mathbb{Z}}}$ and to characterize the generators of $C_{K,2}$.http://periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/31299Unramified extensionsHilbert $2$-Class Field |
| spellingShingle | Mohammed Talbi Abdelmalek Azizi Idriss Jerrari Unramified extensions of some cyclic quartic fields Boletim da Sociedade Paranaense de Matemática Unramified extensions Hilbert $2$-Class Field |
| title | Unramified extensions of some cyclic quartic fields |
| title_full | Unramified extensions of some cyclic quartic fields |
| title_fullStr | Unramified extensions of some cyclic quartic fields |
| title_full_unstemmed | Unramified extensions of some cyclic quartic fields |
| title_short | Unramified extensions of some cyclic quartic fields |
| title_sort | unramified extensions of some cyclic quartic fields |
| topic | Unramified extensions Hilbert $2$-Class Field |
| url | http://periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/31299 |
| work_keys_str_mv | AT mohammedtalbi unramifiedextensionsofsomecyclicquarticfields AT abdelmalekazizi unramifiedextensionsofsomecyclicquarticfields AT idrissjerrari unramifiedextensionsofsomecyclicquarticfields |