The $R_{\infty }$-property for right-angled Artin groups and their nilpotent quotients

Abstract

It is proven that every non-abelian right-angled Artin group has the $R_{\infty }$-property and bounds are given on the $R_{\infty }$-nilpotency index. In case the graph is transposition-free, which is true for almost all graphs, it is shown that the $R_{\infty }$-nilpotency index is equal to 2.

21 pages