$R_{\infty }$-property for finitely generated torsion-free 2-step nilpotent groups of small Hirsch length

Abstract

In this paper we will show that finitely generated torsion-free 2-step nilpotent groups of Hirsch length at most 6 do not have the $R_{\infty }$-property, while there are examples of such groups of Hirsch length 7 that do have the $R_{\infty }$-property.