Index of an open subgroup (awaiting review)

The index of an open subgroup $H$ of a profinite group $G$ is the positive integer $[G:H]$.

When $G$ is a matrix group over $\widehat \Z$ or $\Z_\ell$ and $H$ is a subgroup of level $N$, this is the same as the index of $H$ in the reduction of $G$ modulo $N$.