Separable subgroups have bounded packing

TL;DR

This paper proves that separable subgroups in certain groups have the bounded packing property, answering a question about virtually polycyclic groups and advancing understanding of subgroup structure.

Contribution

It establishes that separable subgroups have bounded packing in ambient groups, including virtually polycyclic groups, providing a positive answer to a previously open question.

Findings

Separable subgroups have bounded packing in ambient groups.

Virtually polycyclic groups' subgroups satisfy bounded packing.

Addresses a question posed by Hruska and Wise.

Abstract

In this note, we prove that separable subgroups have bounded packing in ambient groups. The notion bounded packing was introduced by Hruska and Wise and in particular, our result answers positively a question of theirs, asking whether each subgroup of a virtually polycyclic group has the bounded packing property.