Arithmetic of certain -extensions ramified at three places. II

Abstract

Let be a regular odd prime, the th cyclotomic field and , where is a positive integer. Under the assumption that there are exactly three places not over that ramify in , we continue to study the structure of the Tate module (Iwasawa module) as a Galois module. In the case , we prove that for finite we have for some odd positive integer . Under the same assumptions, if is the Galois group of the maximal unramified Abelian -extension of , then the kernel of the natural epimorphism is of order . Some other results are obtained.