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- W246008113 abstract "Suppose $R$ is a profinite ring. We construct a large class of profinite groups $widehat{{scriptstylebf L}'{scriptstylebf H}_R}mathfrak{F}$, including all soluble profinite groups and profinite groups of finite cohomological dimension over $R$. We show that, if $G in widehat{{scriptstylebf L}'{scriptstylebf H}_R}mathfrak{F}$ is of type $operatorname{FP}_infty$ over $R$, then there is some $n$ such that $H_R^n(G,R [[ G ]]) neq 0$, and deduce that torsion-free soluble pro-$p$ groups of type $operatorname{FP}_infty$ over $mathbb{Z}_p$ have finite rank, thus answering the torsion-free case of a conjecture of Kropholler." @default.
- W246008113 created "2016-06-24" @default.
- W246008113 creator A5073171047 @default.
- W246008113 date "2014-12-05" @default.
- W246008113 modified "2023-09-27" @default.
- W246008113 title "On Profinite Groups of Type $operatorname{FP}_infty$" @default.
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- W246008113 hasPublicationYear "2014" @default.
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