Unramified extensions of quadratic number fields with Galois group $SL_2(7)$
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| _version_ | 1866916613172756480 |
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| author | König, Joachim |
| author_facet | König, Joachim |
| contents | We provide an infinite family of quadratic number fields with everywhere unramified Galois extensions of Galois group $SL_2(7)$. To my knowledge, this is the first instance of infinitely many such realizations for a perfect group which is not generated by involutions, a property which makes it difficult to approach for the problem in question and leads to somewhat delicate local-global problems in inverse Galois theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2109_09646 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Unramified extensions of quadratic number fields with Galois group $SL_2(7)$ König, Joachim Number Theory We provide an infinite family of quadratic number fields with everywhere unramified Galois extensions of Galois group $SL_2(7)$. To my knowledge, this is the first instance of infinitely many such realizations for a perfect group which is not generated by involutions, a property which makes it difficult to approach for the problem in question and leads to somewhat delicate local-global problems in inverse Galois theory. |
| title | Unramified extensions of quadratic number fields with Galois group $SL_2(7)$ |
| topic | Number Theory |
| url | https://arxiv.org/abs/2109.09646 |