# On a theorem of Hegyv\'{a}ri and Hennecart

## TL;DR

This paper investigates the growth rates of product sets in the Heisenberg group over finite fields and complex numbers, providing improvements and extensions to recent related results.

## Contribution

It offers new bounds and generalizations for product set growth in the Heisenberg group, advancing understanding in additive combinatorics.

## Key findings

- Improved bounds on product set growth in the Heisenberg group
- Extended results to complex numbers and finite fields
- Enhanced understanding of combinatorial properties in non-abelian groups

## Abstract

In this paper, we study growth rate of product of sets in the Heisenberg group over finite fields and the complex numbers. More precisely, we will give improvements and extensions of recent results due to Hegyv\'{a}ri and Hennecart (2018).