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|Type:||Artigo de periódico|
|Title:||On a conjecture of E. Rapaport Strasser about knot-like groups and its pro-p version|
|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.|
|Editor:||Elsevier Science Bv|
|Appears in Collections:||Unicamp - Artigos e Outros Documentos|
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