Clarification of absolute Galois group temrinology

Question

In a paper by Mazur, he writes "the profinte group equal to $G_{K,S}$ for some algebraic number field $K$ and finite set of primes $S$ in $K$.

I understand $G_K = \text{Aut}(\overline{K}/K)$ but not how $S$ is relevant or affects the situation. i.e., what is the difference between $G_{K,S}$ and $G_K$.

Thanks.

Answer 1

The $G_{K,S}$ means the Galois group over $K$ of the maximal extension unramified outside $S$.