Cyclotomic Zp-extension
= Cyclotomic Zp-extension
For odd $p$, remove the finite torsion subgroup $\mu_{p-1}$ from the <Galois group> of $\mathbb Q(\mu_{p^\infty})/\mathbb Q$ by taking its fixed field. For $p=2$, take the fixed field of $\{\pm1\}$ instead. The remaining <Galois group> is $\mathbb Z_p$, using the <p-adic logarithm> on $1+p\mathbb Z_p$ or $1+4\mathbb Z_2$. For a <number field> $K$, the cyclotomic Zp-extension is the compositum with this rational tower.