Homological properties of pro-p groups

Author(s)

Aline Gomes da Silva Pinto

• Document type: Doctoral Thesis
• Press: Campinas, SP.
• Institution: Universidade Estadual de Campinas (UNICAMP). Instituto de Matemática, Estatística e Computação Científica
• Defense date: 2005-07-22

Examining board members

Dessislava Hristova Kochloukova; Antonio José Engler; Said Najati Sidki; Pavel Zalesski; Flávio Ulhoa Coelho

• Advisor: Dessislava Hristova Kochloukova

Abstract

In this work, we prove two results about homological properties of metabelian pro-p groups. The first one answers positively a conjecture suggested by J. King that, if G is a finitely generated metabelian pro-p group and m a positive integer, G embeds in a metabelian pro-p group of homological type F P m. The second result caracterize the modules B of homological type F P mover [[ZpG]], where G is a topologically finitely generated metabelian pro-p group that is an extension of A by Q, with A and Q abelian, and B is a finitely generated pro-p [[ZpQ]]-module that is viewed as a pro-p [[ZpG]]-module via the projection G -f Q. The characterization is given in terms of the invariant introduced by J. King [15] and is a generalization of the case when B = Zp is considered as a trivial [[ZpG]]-module, that gives the classification of metabelian pro-p groups of type FPm, proved by D. Kochloukova [18] (AU)