Infinite presentability of groups and condensation (Q2921051)

The authors study finitely generated groups \(G\) from the point of view how they sit in the space of marked groups and similar spaces, with respect to the Chabauty topology. They relate this to group theoretical propeties of \(G\). One focus of the paper is the maximal perfect subset of these spaces, called the set of condensation points. Here, the term perfect is meant in the sense of topology, i.e. a space \(X\) is called perfect if every point of \(X\) is an accumulation point of \(X\). For the spaces under consideration, the set of condensation points is homeomorphic to the Cantor set. The authors describe various classes of groups that are condensation points, in terms of properties of their (infinite) presentations. They prove that every finitely generated infinitely presented metabelian group is a condensation point.