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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}) Click to show full abstract
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:
homology centre;
pro groups;
growth homology;
centre metabelian;
metabelian pro
Journal Title: Canadian Journal of Mathematics
Year Published: 2020
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Journal Title: Canadian Journal of Mathematics
Year Published: 2020
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!