Please use this identifier to cite or link to this item: http://repositorio.unicamp.br/jspui/handle/REPOSIP/69625
Type: Artigo
Title: Homological invariants for pro-p groups and some finitely presented pro-C groups
Author: Kochloukova, Dessislava H.
Zalesskii, Pavel
Abstract: Let G be a finitely presented pro-L group with discrete relations. We prove that the kernel of an epimorphism of G to Z(l) is topologically finitely generated if G does not contain a free pro-L 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 ([15], [17]). For a prop group G of type FP. we define a homological invariant Sigma(m)(G) and prove that this invariant determines when a subgroup H of G that contains the commutator subgroup G' is itself of type FPm. This generalises work of J. King for Sigma(1)(G) in the case when G is metabelian [9]. Both parts of the paper are linked via two conjectures for finitely presented pro-p groups G without free non-cyclic prop subgroups. The conjectures suggest that the above conditions on G impose some restrictions on Sigma(1)(G) and on the automorphism group of G.
Let G be a finitely presented pro-L group with discrete relations. We prove that the kernel of an epimorphism of G to Z(l) is topologically finitely generated if G does not contain a free pro-L group of rank 2. In the case of pro-p groups the result is du
Subject: Teoria dos grupos
Grupos profinitos
Álgebra homológica
Country: Austria
Editor: Springer
Citation: Monatshefte Fur Mathematik. Springer Wien, v. 144, n. 4, n. 285, n. 296, 2005.
Rights: Fechado
Identifier DOI: 10.1007/s00605-004-0269-9
Address: https://link.springer.com/article/10.1007/s00605-004-0269-9
Date Issue: 2005
Appears in Collections:IMECC - Artigos e Outros Documentos

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