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Generic Galois extensions for SL_2(F_5) over Q
Plans Berenguer, Bernat
Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I; Universitat Politècnica de Catalunya. EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions
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 $\widetilde{A_5}\cong \SL_2(\mathbb{F}_5)$.
Peer Reviewed
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
Mathematical Publishing

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