 Zp-extension

A Zp-extension is an infinite Galois extension of a number field whose Galois group is topologically isomorphic to the additive p-adic integers. There is a unique intermediate field of degree $p^n$ for every $n\ge 0$, corresponding to $p^n{\mathbb{Z}}_p$. The finite layers form a tower with cyclic successive degree $p$ extensions.