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

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

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