English

Groups with many finitary cohomology functors

Group Theory 2012-08-07 v1

Abstract

For a group G we consider the set of natural numbers n for which the nth cohomology functor of G commutes with filtered colimit systems of coefficient modules. We find that for the large class of hierarchically decomposable groups there is a dichotomy: this set of natural numbers is either finite or cofinite. Moreover any finite or cofinite set is shown to arise in suitable examples. A survey of recent literature on this topic, especially the work of Martin Hamilton, is included.

Keywords

Cite

@article{arxiv.1208.1008,
  title  = {Groups with many finitary cohomology functors},
  author = {P. H. Kropholler},
  journal= {arXiv preprint arXiv:1208.1008},
  year   = {2012}
}

Comments

16 pages

R2 v1 2026-06-21T21:46:28.300Z