Groups Elementarily Equivalent to a Free 2-nilpotent Group of Finite Rank

TL;DR

This paper characterizes groups that are elementarily equivalent to free nilpotent groups of class 2 with finite rank, providing insights into their logical and algebraic structure.

Contribution

It offers a new characterization of groups elementarily equivalent to free nilpotent groups of class 2 and finite rank, advancing understanding of their model-theoretic properties.

Findings

Characterization of groups elementarily equivalent to free 2-nilpotent groups

Extension of known results to arbitrary finite rank

Insights into the logical structure of such groups

Abstract

In this paper we find a characterization for groups elementarily equivalent to a free nilpotent group $G$ of class 2 and arbitrary finite rank.