Isolated orderings on amalgamated free products

TL;DR

This paper demonstrates that certain amalgamated free products can admit discrete isolated orderings, expanding the known constructions and allowing for many non-trivial convex subgroups.

Contribution

It generalizes previous constructions of isolated orderings to include cases with many non-trivial convex subgroups in amalgamated free products.

Findings

Amalgamated free products can admit discrete isolated orderings under specific conditions.

The construction allows for many non-trivial proper convex subgroups.

This work broadens the class of groups known to have isolated orderings.

Abstract

We show that an amalgamated free product $G*_{A}H$ admits a discrete isolated ordering, under some assumptions of $G,H$ and $A$. This generalizes the author's previous construction of isolated orderings, and unlike known constructions of isolated orderings, can produce an isolated ordering with many non-trivial proper convex subgroups.