dc.contributor
Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I
dc.contributor
Universitat Politècnica de Catalunya. EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions
dc.contributor.author
Plans Berenguer, Bernat
dc.identifier
Plans i Berenguer, Bernat. Generic Galois extensions for SL_2(F_5) over Q. Mathematical research letters, 2007, vol. 14, núm. 3, p. 443-452
dc.identifier
https://hdl.handle.net/2117/1955
dc.description.abstract
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 $\widetilde{A_5}\cong \SL_2(\mathbb{F}_5)$.
dc.description.abstract
Peer Reviewed
dc.format
application/pdf
dc.publisher
Mathematical Publishing
dc.relation
MCYT BFM2003-01898
dc.subject
Field theory (Physics)
dc.subject
Commutative rings
dc.subject
Teoria de cossos
dc.subject
Commutative rings
dc.subject
Galois, Teoria de
dc.subject
Classificació AMS::12 Field theory and polynomials::12F Field extensions
dc.subject
Classificació AMS::13 Commutative rings and algebras::13A General commutative ring theory
dc.title
Generic Galois extensions for SL_2(F_5) over Q
