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|Type:||Artigo de periódico|
|Title:||Profinite And Pro-p Completions Of Poincaré 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 FP m over the field double-struck F signp for a fixed natural prime p (resp. of finite cohomological p-dimension, of finite Euler p-characteristic). We apply our methods for orientable Poincaré duality groups G of dimension 3 and show that the pro-p completion Ĝp of G is a pro-p Poincaré duality group of dimension 3 if and only if every subgroup of finite index in Ĝp has deficiency 0 and Ĝp is infinite. Furthermore if Ĝp is infinite but not a Poincaré duality pro-p group, then either there is a subgroup of finite index in Ĝp of arbitrary large deficiency or Ĝp is virtually double-struck Z signp. Finally we show that if every normal subgroup of finite index in G has finite abelianization and the profinite completion Ĝ of G has an infinite Sylow p-subgroup, then Ĝ is a profinite Poincaré duality group of dimension 3 at the prime p. © 2007 American Mathematical Society.|
|Appears in Collections:||Unicamp - Artigos e Outros Documentos|
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