Mathematics Colloquia and Seminars

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Bounded packing of subgroups of countably infinite groups were defined by Chris Hruska and Dani Wise. A subgroup H of a group G has bounded packing if any collection of pairwise uniformly close left cosets of H is uniformly finite. This holds for separable subgroups of any group, quasi-convex subgroups of hyperbolic groups and so on. Nevertheless, we only know of a relatively few classes of groups and certain classes of subgroups of them for which this is true. Hruska and Wise asked if this is true for all subgroups of solvable groups. In this talk, we will show that bounded packing holds for all subgroups of nilpotent-by-polycyclic groups. Finally, if time permits, we will describe an example of a finitely generated solvable group of derived length 3 that has a finitely generated subgroup without the bounded packing property. Although the statements are geometric, proofs are mostly algebraic and are easily accessible to all.