Packing subgroups in solvable groups
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Packing subgroups in solvable groups

  • Author(s): Sardar, Pranab
  • et al.

Published Web Location

https://arxiv.org/pdf/1408.2311.pdf
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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.

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