Limits of metabelian groups

TL;DR

This paper investigates the limits of certain two-generated groups, specifically abelian-by-infinite cyclic groups, using number theory, and explores their universal equivalence in the space of marked groups.

Contribution

It introduces a novel approach to analyze limits of abelian-by-cyclic groups via number theoretic techniques and examines their universal equivalence.

Findings

Characterization of limits of abelian-by-cyclic groups

Application of number theory to group limits

Discussion of universal equivalence among these limits

Abstract

We describe the two-generated limits of abelian-by-(infinite cyclic) groups in the space of marked groups using number theoretic methods. We also discuss universal equivalence of these limits.