Homological Invariants for pro-p Groups and Some Finitely Presented pro- C Groups

• Autores: Dessislava H. Kochloukova, Pavel A. Zalesskii
• Localización: Monatshefte für mathematik, ISSN 0026-9255, Vol. 144, Nº 4, 2005, págs. 285-296
• Idioma: inglés
• DOI: 10.1007/s00605-004-0269-9
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• Resumen

  • Let G be a finitely presented pro- group with discrete relations. We prove that the kernel of an epimorphism of G to is topologically finitely generated if G does not contain a free pro- 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 pro-p group G of type FPm 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 FPm. This generalises work of J. King for 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 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