# Some remarks on products of sets in the Heisenberg group and in the affine group

## TL;DR

This paper explores the behavior of product sets in the Heisenberg and affine groups over prime fields, providing new growth results and applications to Freiman's isomorphism in nonabelian groups.

## Contribution

It introduces novel results on product set growth in nonabelian groups and applies these findings to Freiman's isomorphism problem.

## Key findings

- New growth results for product sets in the Heisenberg group
- New growth results for product sets in the affine group over prime fields
- Application to Freiman's isomorphism in nonabelian groups

## Abstract

We obtain some new results on products of large and small sets in the Heisenberg group as well as in the affine group over the prime field. Also, we derive an application of these growth results to Freiman's isomorphism in nonabelian groups.