On profinite groups with finite abelianizations

• Autores: Thomas Weigel
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 13, Nº. 1, 2007, págs. 175-181
• Idioma: inglés
• DOI: 10.1007/s00029-007-0035-7
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• Resumen

  • 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 G with this property satisfies [G]) = 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).