Lemma 11.1.
Assuming that:
Δ
⊂
K
∗
∕
(
K
∗
)
n
a finite subgroup
L
=
K
(
Δ
n
)
Then
L
∕
K
is Galois and
Gal
(
L
∕
K
)
≅
Hom
(
Δ
,
μ
n
)
.