# Groups with flat-rank greater than 1

## TL;DR

This paper introduces a general method for identifying subgroups with higher flat-rank in totally disconnected, locally compact groups by leveraging their internal structure, specifically the Levi subgroup, to construct new flat groups.

## Contribution

It presents a novel approach to find subgroups with increased flat-rank using internal structural properties of the group, notably the Levi subgroup.

## Key findings

- Method effectively finds subgroups with flat-rank greater than 1
- Utilizes internal structure to construct new flat groups
- Under certain conditions, increases flat-rank by one

## Abstract

A general method for finding subgroups of a totally disconnected, locally compact groups having flat-rank greater than 1 is described. This method uses the internal structure of the group, notably the Levi subgroup of a given flat group, in order to produce a new flat group that, under an additional hypothesis, has flat-rank one greater than that of the given group.