Talk:Galois group

I'm afraid, this part "The Galois group of a polynomial f over a field F is the Galois group associated to F(α) where α is a root of f. The group obtained does not depend on the choice of root. " , take for instance f(x) = x^6 - 1 <math>\in \mathbb{Q}[x]</math>. Perhaps we introduce the splitting field first? --BRichtigen 16:36, 17 November 2008 (EST)