Selecta Mathematica

, 13:175

On profinite groups with finite abelianizations


DOI: 10.1007/s00029-007-0035-7

Cite this article as:
Weigel, T. Sel. math., New ser. (2007) 13: 175. doi:10.1007/s00029-007-0035-7


Profinite groups with finite p-abelianizations arise in various contexts: group theory, number theory and geometry. Using Ph. Furtwängler’s transfer vanishing theorem it will be proved that a finitely generated profinite group Ĝ with this property satisfies \(H^1(\hat{G}, {\mathbb{F}}_{p}\)Ĝ〛) = 0 (Thm. A). As a consequence one finds that a hereditarily just-infinite non-virtually cyclic pro-p group has only one end (Cor. B). Applied to 3-dimensional Poincaré duality groups, Theorem A yields a generalization of A. Reznikov’s theorem on 3-dimensional co-compact hyperbolic lattices violating W. Thurston’s conjecture (Thm. C).

Mathematics Subject Classification (2000).

Primary 20E18


FAB-groupsends of pro-p groupsPoincaré duality

Copyright information

© Birkhäuser Verlag, Basel/Switzerland 2007

Authors and Affiliations

  1. 1.Università di Milano-BicoccaMilanoItaly