Groups of finite cohomological dimension

Abstract A profinite group G is said to have cohomological dimension at most n if Hr (G, A) is zero for all r > n and all discrete Z-torsion G-modules A. The groups of co omological dimension at most 1 are just the projective groups. Among other important groups which have finite cohomological dimension are the torsion-free profinite groups of finite rank and certain Galois groups Gal (K/k), where K is either a separable closure of k or the subfield of a separable closure generated by all finite Galois extensions of p-power degree.