In
abstract algebra, an
abelian extension is a
Galois extension whose
Galois group is
abelian. When the Galois group is also
cyclic, the extension is also called a
cyclic extension. Going in the other direction, a Galois extension is called
solvable if its Galois group is
solvable, i.e., if the group can be decomposed into a series of normal
extensions of an abelian group.