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Let be a Dedekind domain with field of fractions and a finite group. We show that, if is a ring of -adic integers, then the Witt decomposition map between the Grothendieck-Witt group of bilinear -modules and the one of finite bilinear -modules is surjective. For number fields is also surjective, if is a nilpotent group of odd order, but there are counterexamples for groups of even order.
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