For example, the abelianization (the biggest abelian quotient) Gab of G corresponds to a field referred to as the maximal abelian extension Fab (called so since any further extension is not abelian, i.e., does not have an abelian Galois group).
For example, the abelianization (the biggest abelian quotient) Gab of G corresponds to a field referred to as the maximal abelian extension Fab (λέγονται έτσι αφού κάθε μεγαλύτερη επέκταση δεν είναι αβελιανή, π.χ., δεν έχει αβελιανή ομάδα Galois).