Virtual Lie subgroups of locally compact groups

TL;DR

This paper investigates subgroups of locally compact groups that are images of connected Lie groups, providing new criteria and characterizations to better understand their structure and relationship.

Contribution

It introduces a new criterion for identifying Lie group images within locally compact groups and offers novel characterizations of Lie groups and their images.

Findings

Established a criterion for subgroups to be Lie group images

Provided a new characterization of Lie groups

Characterized groups that are images of connected locally compact groups

Abstract

We examine subgroups of locally compact groups that are continuous homomorphic images of connected Lie groups and we give a criterion for being such an image. We also provide a new characterisation of Lie groups and a characterisation of groups that are images of connected locally compact groups.