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Title:
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Generic Galois extensions for SL_2(F_5) over Q
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Author:
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Plans Berenguer, Bernat
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Other authors:
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Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I; Universitat Politècnica de Catalunya. EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions |
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Abstract:
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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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Abstract:
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Peer Reviewed |
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Subject(s):
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-Field theory (Physics)
-Commutative rings
-Galois theory
-Teoria de cossos
-Commutative rings
-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 |
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Rights:
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Document type:
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Article |
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Published by:
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Mathematical Publishing
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