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The surgery obstruction groups $$L_n(R\pi, w)$$ of C.T.C. Wall [wall-book], [wall-VI] depend on a coefficient ring $R$, a discrete group $\pi$ and an orientation character $w\colon \pi \to \{\pm 1\}$. In general the surgery obstruction groups are abelian groups For finite groups $\pi$ the $L$-groups are

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