Abstract
If the group G of automorphisms s 1, ..., s M of a Galois number field K is an abelian group, i.e. if the automorphisms s i , ..., s M commute with one another, then K is called an abelian field. In particular, if the group G is cyclic, i.e. if all M automorphisms s 1, ..., s M can be represented as powers of a single one of them, then the abelian field K is called a cyclic field.
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