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|Type:||Artigo de periódico|
|Title:||Profinite and pro-p completions of poincare duality groups of dimension 3|
|Abstract:||We establish some sufficient conditions for the profinite and pro-p completions of an abstract group G of type FPm (resp. of finite cohomological dimension, of finite Euler characteristic) to be of type FPm over the field F-p for a fixed natural prime p (resp. of finite cohomological p-dimension, of finite Euler p-characteristic). We apply our methods for orientable Poincare duality groups G of dimension 3 and show that the pro-p completion (G) over capp of G is a pro-p Poincare duality group of dimension 3 if and only if every subgroup of finite index in (G) over capp has deficiency 0 and (G) over capp is infinite. Furthermore if (G) over capp is infinite but not a Poincare duality pro-p group, then either there is a subgroup of finite index in (G) over capp of arbitrary large deficiency or (G) over capp is virtually Z(p). Finally we show that if every normal subgroup of finite index in G has finite abelianization and the profinite completion (G) over cap of G has an infinite Sylow p-subgroup, then (G) over cap is a profinite Poincare duality group of dimension 3 at the prime p.|
|Editor:||Amer Mathematical Soc|
|Appears in Collections:||Artigos e Materiais de Revistas Científicas - Unicamp|
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