On the Pseudo-Cyclicity of Some Iwasawa Modules Associated to Abelian Fields

J. Math. Sci. Univ. Tokyo
Vol. 4 (1997), No. 1, Page 183--209.

Tsuji, Takae
On the Pseudo-Cyclicity of Some Iwasawa Modules Associated to Abelian Fields
Let $p$ be an odd prime number, and $K / \Q$ a totally imaginary finite abelian extension of the first kind, with the Galois group $Î$. Let ${\cal U}_\infty$ (resp. ${\cal E}_\infty$ ) denote the projective limit of the semi-local units (resp. the global units) of the fields in the cyclotomic $\Zp$-extension of $K$. We will show that ${( {\cal U}_\infty / {\cal E}_\infty )}^+$ contains a cyclic $Î [ Î ]$-submodule of finite index.