Extensions with Galois group Hol(C8) unramified over a complex quadratic number field
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909557572239360 |
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| author | Benjamin, Elliot Lemmermeyer, Franz Snyder, Chip |
| author_facet | Benjamin, Elliot Lemmermeyer, Franz Snyder, Chip |
| contents | We study normal extensions with Galois group Hol($C_8$) that are unramified over a complex quadratic subfield. The Galois group is either the semi-dihedral group or the modular group of order $16$. We present an explicit construction of such fields. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_23027 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Extensions with Galois group Hol(C8) unramified over a complex quadratic number field Benjamin, Elliot Lemmermeyer, Franz Snyder, Chip Number Theory 11R20 We study normal extensions with Galois group Hol($C_8$) that are unramified over a complex quadratic subfield. The Galois group is either the semi-dihedral group or the modular group of order $16$. We present an explicit construction of such fields. |
| title | Extensions with Galois group Hol(C8) unramified over a complex quadratic number field |
| topic | Number Theory 11R20 |
| url | https://arxiv.org/abs/2503.23027 |