Separability in Morse local-to-global groups

TL;DR

This paper proves that in Morse local-to-global groups with separable stable subgroups, the product of such subgroups remains separable, with applications to virtually special groups.

Contribution

It establishes the separability of products of stable subgroups in Morse local-to-global groups and applies this to virtually special groups.

Findings

Product of stable subgroups is separable in Morse local-to-global groups.

Separable stable subgroups imply separability of their products.

Application to virtually special groups confirms broader relevance.

Abstract

We show that in a Morse local-to-global group where stable subgroups are separable, the product of any stable subgroups is separable. As an application, we show that the product of stable subgroups in virtually special groups is separable.