Infinite presentability of groups and condensation
Abstract
We describe various classes of infinitely presented groups that are condensation points in the space of marked groups. A well-known class of such groups consists of finitely generated groups admitting an infinite minimal presentation. We introduce here a larger class of condensation groups, called infinitely independently presentable groups, and establish criteria which allow one to infer that a group is infinitely independently presentable. In addition, we construct examples of finitely generated groups with no minimal presentation, among them infinitely presented groups with Cantor-Bendixson rank 1, and we prove that every infinitely presented metabelian group is a condensation group.
Cite
@article{arxiv.1010.0271,
title = {Infinite presentability of groups and condensation},
author = {Robert Bieri and Yves de Cornulier and Luc Guyot and Ralph Strebel},
journal= {arXiv preprint arXiv:1010.0271},
year = {2019}
}
Comments
32 pages, no figure. 1->2 Major changes (the 13-page first version, authored by Y.C. and L.G., was entitled "On infinitely presented soluble groups") 2->3 some changes including cuts in Section 4