On groups with finitely many Conradian orderings

TL;DR

This paper investigates the structure of groups with finitely many Conradian orderings, establishing a link between isolated left-orderings and the finiteness of the entire set of left-orderings.

Contribution

It proves that in groups with finitely many Conradian orderings, an isolated left-ordering exists if and only if the group has finitely many left-orderings.

Findings

Having an isolated left-ordering is equivalent to having finitely many left-orderings.

The study characterizes the space of left-orderings for this class of groups.

Provides a criterion linking isolated orderings to the finiteness of the ordering space.

Abstract

We study the space of left-orderings on groups with finitely many Conradian orderings. We show that, within this class of groups, having an isolated left-ordering is equivalent to having finitely many left-orderings.