The $R_{\infty }$ property for crystallographic group of Sol

Abstract

There are 9 kinds of crystallographic groups $\Pi$ of Sol. For any automorphism $\phi$ on $\Pi$, we study the Reidemeister number $R(\phi )$. Using the averaging formula for the Reidemeister numbers, we prove that most of the crystallographic groups of Sol have the $R_{\infty }$ property.

25 pages