English

Groups elementarily equivalent to metabelian Baumslag$-$Solitar groups and regular bi-interpretability

Group Theory 2024-07-02 v1 Logic

Abstract

We prove that metabelian Baumslag-Solitar group BS(1,k)BS(1,k), k>1k>1, is (strongly) regularly bi-interpretable with the ring of integers Z\mathbb{Z}, and describe in algebraic terms all groups that are elementarily equivalent to BS(1,k)BS(1,k).

Keywords

Cite

@article{arxiv.2407.00642,
  title  = {Groups elementarily equivalent to metabelian Baumslag$-$Solitar groups and regular bi-interpretability},
  author = {Evelina Daniyarova and Alexei Myasnikov},
  journal= {arXiv preprint arXiv:2407.00642},
  year   = {2024}
}
R2 v1 2026-06-28T17:23:56.955Z