On the Isomorphism classes of Iwasawa modules with $\lambda = 3$ and $\mu = 0$

Abstract

For an odd prime number $p$, we classify the isomorphism classes of finitely generated torsion $\Lambda=\mathbb{Z}_{p}[[T]]$-modules with $\lambda=3$ and $\mu=0$, which are free over $\mathbb{Z}_{p}$. We apply this classification to the Iwasawa module associated to the cyclotomic $\mathbb{Z}_{p}$-extension of an imaginary quadratic field.