# Locally compact wreath products

## TL;DR

This paper extends the wreath product construction to locally compact groups, enabling new examples of groups with intermediate growth and no nontrivial compact normal subgroups, thus advancing the understanding of their structure.

## Contribution

It introduces a natural extension of wreath products to locally compact groups and constructs new examples disproving a conjecture about groups of intermediate growth.

## Key findings

- Extended wreath product construction to locally compact groups
- Constructed examples of groups with intermediate growth
- Disproved Trofimov's conjecture on compactly generated groups

## Abstract

Wreath products of non-discrete locally compact groups are usually not locally compact groups, nor even topological groups. We introduce a natural extension of the wreath product construction to the setting of locally compact groups. As an application, we disprove a conjecture of Trofimov, constructing compactly generated locally compact groups of intermediate growth without nontrivial compact normal subgroups.