# A sufficient condition for a locally compact almost simple group to have open monolith

## TL;DR

This paper provides a sufficient condition for a totally disconnected, locally compact group with a topologically simple monolith to have that monolith be open and abstractly simple, advancing understanding of the structure of such groups.

## Contribution

It introduces a new criterion that guarantees the openness and simplicity of the monolith in totally disconnected, locally compact groups.

## Key findings

- The monolith is open under the given condition.
- The monolith is shown to be abstractly simple.
- The paper advances structural understanding of locally compact groups.

## Abstract

We obtain a sufficient condition, given a totally disconnected, locally compact group $G$ with a topologically simple monolith $S$, to ensure that $S$ is open in $G$ and abstractly simple.