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Let p be a prime number, T a class of finite groups closed under extensions, subgroups and quotients, and suppose that the cyclic group of order p is in T. We find some sufficient and necessary conditions for the pro-T completion of an abstract orientable Poincare duality group G of dimension 4 and Euler characteristic 0 to be a profinite orientable Poincare duality group of dimension 4 at the prime p with Euler p-characteristic 0. In particular we show that the pro-p completion y Gp of G is an orientable Poincare duality pro-p group of dimension 4 and Euler characteristic 0 if and only if G is p-good.

Profinite completions of orientable Poincaré duality groups of dimension four and Euler characteristic zero