Commensurability and bi-interpretability of groups

TL;DR

This paper explores the relationship between commensurable groups and bi-interpretability, demonstrating that under certain definability conditions, these groups are bi-interpretable, which has implications for understanding their structural similarities.

Contribution

It establishes that commensurable groups are bi-interpretable under specific definability conditions, linking two important concepts in group theory and model theory.

Findings

Commensurable groups are bi-interpretable under certain conditions.

Defines the necessary definability conditions for bi-interpretability.

Provides a framework connecting group commensurability and bi-interpretability.

Abstract

Commensurable groups are bi-interpretable, under suitable definability conditions.