Geodesic
Growth of Homology of Centre-by-metabelian Pro-$p$ Groups
Canadian journal of mathematics, Tome 72 (2020) no. 1, pp. 203-224

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DOI

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 $V=\dim V\otimes _{\mathbb{Z}_{p}}\mathbb{Q}_{p}$.
DOI : 10.4153/CJM-2018-032-4
Mots-clés : pro-p group, metabelian group, homology 
Kochloukova, Dessislava H.; Pinto, Aline G. S. Growth of Homology of Centre-by-metabelian Pro-$p$ Groups. Canadian journal of mathematics, Tome 72 (2020) no. 1, pp. 203-224. doi: 10.4153/CJM-2018-032-4
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     author = {Kochloukova, Dessislava H. and Pinto, Aline G. S.},
     title = {Growth of {Homology} of {Centre-by-metabelian} {Pro-}$p$ {Groups}},
     journal = {Canadian journal of mathematics},
     pages = {203--224},
     year = {2020},
     volume = {72},
     number = {1},
     doi = {10.4153/CJM-2018-032-4},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-2018-032-4/}
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