Please use this identifier to cite or link to this item: http://repositorio.unicamp.br/jspui/handle/REPOSIP/67576
Type: Artigo de periódico
Title: On a conjecture of E. Rapaport Strasser about knot-like groups and its pro-p version
Author: Kochloukova, DH
Abstract: A group G is knot-like if it is finitely presented of deficiency 1 and has abelianization G/G' similar or equal to Z. We prove the conjecture of E. Rapaport Strasser that if a knot-like group G has a finitely generated commutator subgroup G' then G' should be free in the special case when the commutator G' is residually finite. It is a corollary of a much more general result : if G is a discrete group of geometric dimension n with a finite K(G, I)-complex Y of dimension n, Y has Euler characteristics 0, N is a normal residually finite subgroup of G, N is of homological type FPn-1 and G/N similar or equal to Z then N is of homological type FP and hence GIN has finite virtual cohomological dimension vcd(GIN) = cd (G) - cd (N). In particular either N has finite index in G or cd(N) <= cd (G) - I. Furthermore we show a pro-p version of the above result with the weaker assumption that GIN is a pro-p group of finite rank. Consequently a pro-p version of Rapaport's conjecture holds. (c) 2005 Elsevier B.V. All rights reserved.
Country: Holanda
Editor: Elsevier Science Bv
Rights: fechado
Identifier DOI: 10.1016/j.jpaa.2005.06.008
Date Issue: 2006
Appears in Collections:Unicamp - Artigos e Outros Documentos

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