Co-Hopfian virtually free groups and elementary equivalence

TL;DR

This paper establishes that co-Hopfian finitely generated virtually free groups are elementarily equivalent only when they are isomorphic, and demonstrates their homogeneity in model theory, advancing understanding of their algebraic and logical properties.

Contribution

It proves the equivalence between elementary equivalence and isomorphism for co-Hopfian virtually free groups and shows their homogeneity in model theory, a novel insight in group theory and logic.

Findings

Elementary equivalence implies isomorphism for these groups

Co-Hopfian virtually free groups are homogeneous in model theory

The results link algebraic structure with logical properties

Abstract

We prove that two co-Hopfian finitely generated virtually free groups are elementarily equivalent if and only if they are isomorphic. We also prove that co-Hopfian finitely generated virtually free groups are homogeneous in the sense of model theory.