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|Type:||Artigo de periódico|
|Title:||Homological Invariants For Pro-p Groups And Some Finitely Presented Pro-script C Sign Groups|
|Abstract:||Let G be a finitely presented pro-script C sign group with discrete relations. We prove that the kernel of an epimorphism of G to ℤ̂script C sign is topologically finitely generated if G does not contain a free pro-script C sign group of rank 2. In the case of pro-p groups the result is due to J. Wilson and E. Zelmanov and does not require that the relations are discrete (, ). For a pro-p group G of type FP m we define a homological invariant ∑m(G) and prove that this invariant determines when a subgroup H of G that contains the commutator subgroup G′ is itself of type FP m . This generalises work of J. King for ∑1(G) in the case when G is metabelian . Both parts of the paper are linked via two conjectures for finitely presented pro-p groups G without free non-cyclic pro-p subgroups. The conjectures suggest that the above conditions on G impose some restrictions on ∑1(G) and on the automorphism group of G. © 2005 Springer-Verlag/Wien.|
|Appears in Collections:||Unicamp - Artigos e Outros Documentos|
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