Presentability by products for some classes of groups
Abstract
In various classes of infinite groups, we identify groups that are presentable by products, i.e. groups having finite index subgroups which are quotients of products of two commuting infinite subgroups. The classes we discuss here include groups of small virtual cohomological dimension and irreducible Zariski dense subgroups of appropriate algebraic groups. This leads to applications to groups of positive deficiency, to fundamental groups of three-manifolds and to Coxeter groups. For finitely generated groups presentable by products we discuss the problem of whether the factors in a presentation by products may be chosen to be finitely generated.
Cite
@article{arxiv.1409.7268,
title = {Presentability by products for some classes of groups},
author = {P. de la Harpe and D. Kotschick},
journal= {arXiv preprint arXiv:1409.7268},
year = {2017}
}
Comments
small edits and addition of an appendix in v2, now 20 pages; added Remark 4.6 suggested by a referee in v3; to appear, without the appendix, in the Journal of Topology and Analysis