CIRCULAR UNITS OF ABELIAN FIELDS WITH A PRIME POWER CONDUCTOR

For an abelian extension K of ${\mathbb{Q}}$, let $C_W(K)$ be the group of Washington units of K, and $C_S(K)$ the group of Sinnott units of K. A lot of results about $C_S(K)$ have been found while very few is known about $C_W(K)$. This is mainly because elements in $C_S(K)$ are more explicitly defined than those in $C_W(K)$. The aim of this paper is to find a basis of $C_W(K)$ and use it to compare $C_W(K)$ and $C_S(K)$ when K is a subfield of ${\mathbb{Q}}({\zeta}_{p^e})$, where p is a prime.