Year: 2014
Type: preprint
Abstract: We show that any subgroup of a (virtually) nilpotent-by-polycyclic group satisfies the bounded packing property of Hruska-Wise. In particular, the same is true about metabelian groups and linear solvable groups. However, we find an example of a finitely generated solvable group of derived length 3 which admits a finitely generated subgroup without the bounded packing property. In this example the subgroup is a metabelian retract also. Thus we obtain a negative answer to Problem 2.27 of Hruska-Wise. On the other hand, we show that polycyclic subgroups of solvable groups satisfy the bounded packing property.
Source: arXiv (Cornell University)
Author: Sardar, Pranab
Institution: University of California, Davis
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2950269447