Generic Galois extensions for SL_2(F_5) over Q
Let $G_n$ be a double cover of either the alternating group $A_n$ or the symmetric group $S_n$, and let $G_{n-1}$ be the corresponding double cover of $A_{n-1}$ or $S_{n-1}$. For every odd $n\geq 3$ and every field $k$ of characteristic $0$, we prove that the following are equivalent: {\bf (i)} ther...
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| Formato: | artículo |
| Fecha de publicación: | 2007 |
| País: | España |
| Recursos: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/1955 |
| Acesso em linha: | https://hdl.handle.net/2117/1955 |
| Access Level: | acceso abierto |
| Palavra-chave: | Field theory (Physics) Commutative rings Galois theory Teoria de cossos Galois, Teoria de Classificació AMS::12 Field theory and polynomials::12F Field extensions Classificació AMS::13 Commutative rings and algebras::13A General commutative ring theory |
| Resumo: | Let $G_n$ be a double cover of either the alternating group $A_n$ or the symmetric group $S_n$, and let $G_{n-1}$ be the corresponding double cover of $A_{n-1}$ or $S_{n-1}$. For every odd $n\geq 3$ and every field $k$ of characteristic $0$, we prove that the following are equivalent: {\bf (i)} there exists a generic extension for $G_{n-1}$ over $k$, {\bf (ii)} there exists a generic extension for $G_n$ over $k$. As a consequence, there exists a generic extension over $\Q$ for the group $\widetilde{A_5}\cong \SL_2(\mathbb{F}_5)$. |
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