Exercise 9.1.7 (Abelian Galois group)

Question

In the last sentence of that proof, how exactly does it `follow'?

Hassaan Naeem · Accepted Answer

extbf{Solution:}
We have that $\phi , 	heta \in Gal_{\mathbb{Q}}(t^n - 1) = Gal(SF_{\mathbb{Q}}(t^n - 1): \mathbb{Q}) = Gal(\mathbb{Q}(\omega): \mathbb{Q})$.
Then by 	extbf{Lemma 4.3.6} we have that if $(	heta \circ \phi)(a)$ = $(\phi \circ 	heta)(a)$, then $	heta \circ \phi = \phi \circ 	heta$.

Exercise 9.1.7 (Abelian Galois group)

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Exercise 9.1.7 (Abelian Galois group)

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