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

  • Dessislava H. Kochloukova (a1) and Aline G. S. Pinto (a2)

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 $V=\dim V\otimes _{\mathbb{Z}_{p}}\mathbb{Q}_{p}$ .

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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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Canadian Journal of Mathematics
  • ISSN: 0008-414X
  • EISSN: 1496-4279
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