abelian extension
Let K be a Galois extension of F. The extension
is said to be an
abelian extension
if the Galois group
Gal(K/F) is abelian
.
Examples: ℚ(√2)/ℚ has Galois group ℤ/2ℤ so ℚ(√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/nℤ)* (the group of units of ℤ/nℤ) so ℚ(ζn)/ℚ is abelian.
Title | abelian extension |
---|---|
Canonical name | AbelianExtension |
Date of creation | 2013-03-22 13:09:28 |
Last modified on | 2013-03-22 13:09:28 |
Owner | scanez (1021) |
Last modified by | scanez (1021) |
Numerical id | 5 |
Author | scanez (1021) |
Entry type | Definition |
Classification | msc 12F10 |
Related topic | KroneckerWeberTheorem |
Related topic | KummerTheory |