Instability of the virtual solvability and the property of being virtually torsion-free for quasi-isometric groups. (English) Zbl 0979.20034
The main results of this paper are: (1) There exist quasi-isometric groups \(G\) and \(H\) such that \(G\) is solvable but \(H\) is not virtually solvable. (2) There exist quasi-isometric groups \(G\) and \(H\) such that \(G\) has no torsion but no subgroup of finite index in \(H\) is torsion-free. This shows that virtual solvability and the property of being virtually torsion-free are not geometric properties.
Reviewer: Wim Malfait (Kortrijk)
MSC:
20F10 | Word problems, other decision problems, connections with logic and automata (group-theoretic aspects) |
20F16 | Solvable groups, supersolvable groups |
20F65 | Geometric group theory |