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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2309.00880 |
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| _version_ | 1866914673157210112 |
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| author | Gow, Rod McGuire, Gary |
| author_facet | Gow, Rod McGuire, Gary |
| contents | We realize Frobenius conjugacy classes in Galois groups of certain $q$-polynomials over $\mathbb{F}_q(t)$ using specific degree 1 ideals. We combine this with methods from elementary linear algebra and group theory to realize transvections in some linear Galois groups. This enables the Galois group to be identified as a known classical group in several reasonably general cases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_00880 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Realizing cyclic linear transformations as Frobenius elements in the Galois groups of $q$-polynomials over function fields Gow, Rod McGuire, Gary Number Theory 11R58 We realize Frobenius conjugacy classes in Galois groups of certain $q$-polynomials over $\mathbb{F}_q(t)$ using specific degree 1 ideals. We combine this with methods from elementary linear algebra and group theory to realize transvections in some linear Galois groups. This enables the Galois group to be identified as a known classical group in several reasonably general cases. |
| title | Realizing cyclic linear transformations as Frobenius elements in the Galois groups of $q$-polynomials over function fields |
| topic | Number Theory 11R58 |
| url | https://arxiv.org/abs/2309.00880 |