When is Group Cohomology Finitary?

dc.creatorHamilton, Martin
dc.date2008-03-17
dc.date.accessioned2026-07-07T09:27:18Z
dc.date.available2026-07-07T09:27:18Z
dc.descriptionIf $G$ is a group, then we say that the functor $H^n(G,-)$ is finitary if it commutes with all filtered colimit systems of coefficient modules. We investigate groups with cohomology almost everywhere finitary; that is, groups with $n$th cohomology functors finitary for all sufficiently large $n$. We establish sufficient conditions for a group $G$ possessing a finite dimensional model for $e.g.$ to have cohomology almost everywhere finitary. We also prove a stronger result for the subclass of groups of finite virtual cohomological dimension, and use this to answer a question of Leary and Nucinkis. Finally, we show that if $G$ is a locally (polycyclic-by-finite) group, then $G$ has cohomology almost everywhere finitary if and only if $G$ has finite virtual cohomological dimension and the normalizer of every non-trivial finite subgroup of $G$ is finitely generated.
dc.description26 pages
dc.identifierhttps://arxiv.org/abs/0803.2540
dc.identifierhttp://arxiv.org/abs/0803.2540
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/157052
dc.subjectGroup Theory
dc.subjectK-Theory and Homology
dc.subject20J06; 20J05; 18G15
dc.titleWhen is Group Cohomology Finitary?
dc.typetext

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