On the realization of subgroups of $PGL(2,F)$, and their automorphism groups, as Galois groups over function fields
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arXiv
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| Format: | Preprint |
| Published: |
2021
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| _version_ | 1866909386869309440 |
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| author | Gow, Rod McGuire, Gary |
| author_facet | Gow, Rod McGuire, Gary |
| contents | Let $F$ be any field. We give a short and elementary proof that any finite subgroup $G$ of $PGL(2,F)$ occurs as a Galois group over the function field $F(x)$. We also develop a theory of descent to subfields of $F$. This enables us to realize the automorphism groups of finite subgroups of $PGL(2,F)$ as Galois groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2109_06693 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | On the realization of subgroups of $PGL(2,F)$, and their automorphism groups, as Galois groups over function fields Gow, Rod McGuire, Gary Number Theory Algebraic Geometry Group Theory 12F12, 11S20 Let $F$ be any field. We give a short and elementary proof that any finite subgroup $G$ of $PGL(2,F)$ occurs as a Galois group over the function field $F(x)$. We also develop a theory of descent to subfields of $F$. This enables us to realize the automorphism groups of finite subgroups of $PGL(2,F)$ as Galois groups. |
| title | On the realization of subgroups of $PGL(2,F)$, and their automorphism groups, as Galois groups over function fields |
| topic | Number Theory Algebraic Geometry Group Theory 12F12, 11S20 |
| url | https://arxiv.org/abs/2109.06693 |