Reidemeister spectrum for metabelian groups of the form {Q}^nrtimes mathbb Z and {mathbb Z[1/p]}^nrtimes mathbb Z, p prime

In this note we study the Reidemeister spectrum for metabelian groups of the form ${\mathbb Q}^n\rtimes \mathbb Z$ and ${\mathbb Z[1/p]}^n\rtimes \mathbb Z$. Particular attention is given to the $R_{\infty}$ property of a subfamily of these groups. We also define a Nielsen spectrum of a space and discuss some examples.