On profinite groups with finite abelianizations |
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Authors: | Thomas Weigel |
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Affiliation: | (1) Università di Milano-Bicocca, U5-3067, Via R. Cozzi, 53, 20125 Milano, Italy |
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Abstract: | Profinite groups with finite p-abelianizations arise in various contexts: group theory, number theory and geometry. Using Ph. Furtw?ngler’s transfer vanishing theorem it will be proved that a finitely generated profinite group Ĝ with this property satisfies 〚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). |
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Keywords: | Primary 20E18 |
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