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 Ξ
k 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 Ξ
k.
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