Rationality questions: examples
Let G be a finite group of order g, and let m be a multiple of the orders of all the elements of G. Take as ground field K the field Q of rational numbers, and let Q(m) be the field obtained by adjoining the mth roots of unity to Q. The Galois group of Q(m) over Q is the group denoted Γ Q in 12.4; it is a subgroup of the group (Z/mZ)*. In fact:
Theorem (Gauss). We have Γ Q = (Z/mZ)*.
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