2008/03/17 by Martin Hamilton, Hamilton, Martin
Mathematics · #18G15 #20J05 #20J06 #Algebraic structures and combinatorial models #Commutative Algebra and Its Applications #FOS: Mathematics #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT) #math.GR #math.KT #msc:18G15 #msc:20J05 #msc:20J06
paper · pdf · doi:10.48550/arxiv.0803.2540
26 pages
arxiv created 2008/03/17 · openalex publication_date 2008/03/17 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
If G is a group, then we say that the functor Hn(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 nth 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.