Locally normal subgroups of simple locally compact groups

TL;DR

This paper investigates the structure of simple locally compact groups, introducing a local invariant called the structure lattice that captures key aspects of their global structure through compact subgroups.

Contribution

It introduces the structure lattice as a new local invariant for simple locally compact groups, linking local subgroup properties to the overall group structure.

Findings

The structure lattice reflects the global structure of the group.

Properties of the structure lattice reveal insights into the group's composition.

The paper provides results on the structure of compactly generated simple locally compact groups.

Abstract

We announce various results concerning the structure of compactly generated simple locally compact groups. We introduce a local invariant, called the structure lattice, which consists of commensurability classes of compact subgroups with open normaliser, and show that its properties reflect the global structure of the ambient group.