abelian extension (original) (raw)

Examples: ℚ⁢(2)/ℚ has Galois group ℤ/2⁢ℤ soℚ⁢(2)/ℚ is an abelian extension.

Let ζn be a primitive nth root of unity (http://planetmath.org/RootOfUnity). Then ℚ⁢(ζn)/ℚ has Galois group (ℤ/n⁢ℤ)* (the group of units ofℤ/n⁢ℤ) so ℚ⁢(ζn)/ℚ is abelian.