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Nella sua memoria sulla risolubilità delle equazioni polinomiali (Mémoire sur les conditions de ré solubilité des équations par radicaux, 1830), Galois definì il gruppo di un polinomio a coefficienti razionali con radici complesse α1,..., α n , come il sottogruppo di S n costituito da tutte quelle permutazioni σ con la proprietà che, per ogni funzione razionale h(X1,..., Xn) ∈ ℚ(X1,..., X n ),

$$ h(\alpha _1 ,...,\alpha _n ) = h(\alpha _{\sigma (1)} ,....,\alpha _{\sigma (n)} ) \Leftrightarrow h(\alpha _1 ,...,\alpha _n ) \in \mathbb{Q}.$$

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© 2008 Springer-Verlag Italia, Milano

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Gabelli, S. (2008). Il gruppo di Galois di un polinomio. In: Teoria delle Equazioni e Teoria di Galois. UNITEXT(). Springer, Milano. https://doi.org/10.1007/978-88-470-0619-5_8

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