Laan, Harmke van der (2022) The CM class number one problem for sextic CM-fields with Galois group (C_2)^3 ⋊ C_3. Master's Thesis / Essay, Mathematics.
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Abstract
In this thesis we discuss the CM class number one problem for sextic CM fields K whose Galois closure has degree 24 over the rational numbers. We establish relations between the discriminants and the relative class numbers of K, its reflex fields and their subfields. We give a full ramification table of primes in K and its reflex fields and derive sufficient conditions for K to have CM class number one. Furthermore, we prove that there exist finitely many sextic CM-fields whose Galois closure has degree 24 over the rational numbers such that they have CM class number one. Finally we give some CM class number one fields of this form.
| Item Type: | Thesis (Master's Thesis / Essay) |
|---|---|
| Supervisor name: | Kilicer, P. and Top, J. |
| Degree programme: | Mathematics |
| Thesis type: | Master's Thesis / Essay |
| Language: | English |
| Date Deposited: | 24 Jan 2022 12:40 |
| Last Modified: | 24 Jan 2022 12:40 |
| URI: | https://fse.studenttheses.ub.rug.nl/id/eprint/26489 |
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