>>26
つづき

>We will see later on how to obtain these expressions for the roots.

これが、12. Groups II: Symmetries of Fields ....69>>25なんだ
で、P76(12.18)に同じ図が出てくる
Returning to some of the other examples from the first lecture, the extension Q ⊂ Q(, !)
satisfies the criterion of the Theorem above, where = √5 2 and ! is a primitive 5-th root of 1. Thus
an automorphism is free to send to any root of the polynomial x5 ? 2 and ! to any root of the 5-th
cyclotomic polynomial 1+x+x^2+x^3+x^4. Thus there are twenty elements of the Galois group in total.