When is Group Cohomology Finitary?
| dc.creator | Hamilton, Martin | |
| dc.date | 2008-03-17 | |
| dc.date.accessioned | 2026-07-07T09:27:18Z | |
| dc.date.available | 2026-07-07T09:27:18Z | |
| dc.description | If $G$ 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.description | 26 pages | |
| dc.identifier | https://arxiv.org/abs/0803.2540 | |
| dc.identifier | http://arxiv.org/abs/0803.2540 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/157052 | |
| dc.subject | Group Theory | |
| dc.subject | K-Theory and Homology | |
| dc.subject | 20J06; 20J05; 18G15 | |
| dc.title | When is Group Cohomology Finitary? | |
| dc.type | text |