Amenable subgroups of Homeo(R) with large characterizing quotients

TL;DR

This paper constructs a finitely generated solvable subgroup of Homeo(R) that has a non-metabelian quotient, providing insights into the structure of such groups and their quotients.

Contribution

It introduces a specific example of a finitely generated solvable subgroup of Homeo(R) with a large, non-metabelian characterizing quotient, advancing understanding of subgroup structures.

Findings

Existence of finitely generated solvable subgroups with complex quotients

Construction of a subgroup with a non-metabelian quotient

Insights into the structure of amenable subgroups of Homeo(R)

Abstract

We construct a finitely generated solvable subgroup of Homeo(R) with a non-metaabelian characterizing quotient.