Groups with the same cohomology as their profinite completions

Karl Lorensen

Groups with the same cohomology as their profinite completions

Group Theory 2010-09-16 v6 K-Theory and Homology

Authors: Karl Lorensen

Abstract

For any positive integer $n$ , $\mathcal{A}_n$ is the class of all groups $G$ such that, for $0\leq i\leq n$ , $H^i(\hat{G},A)\cong H^i(G,A)$ for every finite discrete $\hat{G}$ -module $A$ . We describe certain types of free products with amalgam and HNN extensions that are in some of the classes $\mathcal{A}_n$ . In addition, we investigate the residually finite groups in the class $\mathcal{A}_2$ .

Keywords

group cohomology profinite completion free products with amalgam HNN extensions residually finite groups finite discrete modules

Cite

@article{arxiv.0802.0118,
  title  = {Groups with the same cohomology as their profinite completions},
  author = {Karl Lorensen},
  journal= {arXiv preprint arXiv:0802.0118},
  year   = {2010}
}

Comments

The final version corrects several misprints that appeared in the published version. In addition, it remedies some mistaken attributions regarding quasipotent groups

Groups with the same cohomology as their profinite completions

Abstract

Keywords

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