Zp-extension
= Zp-extension
{c}
{title2=$\operatorname{Gal}(F_\infty/F)\cong\mathbb Z_p$}
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 $n\geq0$, corresponding to $p^n\mathbb Z_p$. The finite layers form a tower with cyclic successive degree $p$ extensions.