On $p$-closed algebraic number fields with restricted ramification

Normal extensions $K$ of a given number field $k$, which are unramified outside a given set $S$ of divisors and are for a fixed prime $p$ closed under $p$-extensions, are considered in the paper. It is assumed that $S$ contains all Archimedean places and all prime divisors of $p$. The cohomology group $H^2(K/k, Z/pZ)$is described, and it is proved that the cohomological $p$-dimension of the Galois group $K/k$ does not exceed 2.
Bibliography: 9 items.