Solvable Subgroups of Locally Compact Groups

TL;DR

This paper proves that closed solvable subgroups of connected Lie groups are compactly generated and discusses extensions of these results to more general locally compact groups.

Contribution

It establishes that closed solvable subgroups in connected Lie groups are compactly generated and explores generalizations to locally compact groups.

Findings

Closed solvable subgroups of connected Lie groups are compactly generated

Discrete solvable subgroups are finitely generated

Extensions to locally compact groups are discussed

Abstract

It is shown that a closed solvable subgroup of a connected Lie group is compactly generated. In particular, every discrete solvable subgroup of a connected Lie group is finitely generated. Generalizations to locally compact groups are discussed as far as they carry.