Bieri, Robert
Cornulier, Yves
Guyot, Luc
Strebel, Ralph
Infinite Presentability Of Groups And Condensation
Journal Of The Institute Of Mathematics Of Jussieu
1474-7480
10.1017/S1474748013000327
13
4
811-848
38
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.
Cantor-Bendixson rank;
condensation group;
infinitely presented metabelian group;
invariant Sigma;
Thompson's group F;
space of marked groups;
Cambridge Univ Press
Cambridge
2014