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Growth of Homology of Centre-by-metabelian Pro-$p$ Groups

Part of: Connections with homological algebra and category theory

Published online by Cambridge University Press:  09 January 2019

Dessislava H. Kochloukova  and
Aline G. S. Pinto
Dessislava H. Kochloukova
Affiliation:
Department of Mathematics, State University of Campinas (UNICAMP), 13083-859 Campinas-SP, Brazil Email: desi@ime.unicamp.br
Aline G. S. Pinto
Affiliation:
Department of Mathematics, University of Brasília, 70297-400 Brasília, Brazil Email: pinto.aline@gmail.com
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Abstract

For a centre-by-metabelian pro-$p$ group $G$ of type $\text{FP}_{2m}$, for some $m\geqslant 1$, we show that $\sup _{M\in {\mathcal{A}}}$ rk $H_{i}(M,\mathbb{Z}_{p})<\infty$, for all $0\leqslant i\leqslant m$, where ${\mathcal{A}}$ is the set of all subgroups of $p$-power index in $G$ and, for a finitely generated abelian pro-$p$ group $V$, rk $V=\dim V\otimes _{\mathbb{Z}_{p}}\mathbb{Q}_{p}$.

Keywords

pro-p groupmetabelian grouphomology

MSC classification

Primary: 20J05: Homological methods in group theory
Type
Article
Information
Canadian Journal of Mathematics , Volume 72 , Issue 1 , February 2020 , pp. 203 - 224
Copyright
© Canadian Mathematical Society 2018 

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Footnotes

Author D. H. K. was partially supported by “bolsa de produtividade em pesquisa” 303350/2013-0 CNPq, Brazil and “projeto de pesquisa regular” FAPESP 2016/05678-3; author A. G. S. P. was partially supported by “Projeto Universal 482658/2013-4” from CNPq, Brazil.

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