Demushkin group

In mathematical group theory, a Demushkin group (also written as Demuškin or Demuskin) is a pro-"p" group "G" having a certain properties relating to duality in group cohomology. More precisely, "G" must be such that the first cohomology group with coefficients in F"p" = Z/"p" Z has finite rank, the second cohomology group has rank 1, and the cup product induces a non-degenerate pairing
Such groups were introduced by .
Demushkin groups occur as the Galois groups of the maximal "p"-extensions of local number fields containing all "p"-th roots of unity.