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Growth of Homology of Centre-by-metabelian Pro-
$p$ Groups
Published online by Cambridge University Press: 09 January 2019
Abstract
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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
MSC classification
- Type
- Article
- Information
- Copyright
- © Canadian Mathematical Society 2018
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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