Circular units of an abelian field ramified at three primes

This paper constructs a basis and gives a presentation of Sinnott's group of circular units for a real abelian field k ramified at three primes whose genus field K   in the narrow sense has cyclic relative Galois group Gal(K/k)Gal(K/k). It is shown that, for this type of fields, the quotient of the module of all relations satisfied by circular units by the submodule generated by all norm relations is a cyclic module generated by an Ennola relation.