We consider an admissible system ({\\mathfrak g},(G,M)) where {\\mathfrak g} is the group of a Galois extension k⁄Q of number fields, G the ring {\\mathcal O}k of integers of k and M=({\\mathcal O}k)2. The cohomology group H1({\\mathfrak g},{\\mathcal O}k) is nicely described by a naive submodule Ξk of {\\mathcal O}k and the Poincaré index iγ({\\mathfrak g},M), γ∈H1({\\mathfrak g},{\\mathcal O}k), for the system ({\\mathfrak g},(G,M)), can be expressed in terms of Ξk.
