Demushkin group
In mathematical group theory, a Demushkin group (also written as Demuškin or Demuskin) is a pro-p group G {\displaystyle G} having a certain properties relating to duality in group cohomology. More precisely, G {\displaystyle G} must be such that the first cohomology group with coefficients in F p = Z / p Z {\displaystyle \mathbb {F} _{p}=\mathbb {Z} /p\mathbb {Z} } has finite rank, the second cohomology group has rank 1, and the cup product induces a non-degenerate pairing H 1 ( G , F p ) × H 1 ( G , F p ) → H 2 ( G , F p ) .