On embeddings into compactly generated groups

TL;DR

This paper demonstrates the existence of a second countable locally compact group that cannot be embedded as a closed subgroup into any compactly generated locally compact group, highlighting limitations in embedding properties.

Contribution

It establishes the existence of a specific second countable locally compact group with non-embedding properties into compactly generated groups.

Findings

Existence of a second countable locally compact group that does not embed into any compactly generated group

Discussion of related embedding and non-embedding results in the context of locally compact groups

Abstract

We prove that there is a second countable locally compact group that does not embed as a closed subgroup in any compactly generated locally compact group, and discuss various related embedding and non-embedding results.