Bitwisted Burnside-Frobenius theorem and Dehn conjugacy problem

Abstract

It is proved for Abelian groups that the Reidemeister coincidence number of two endomorphisms $\phi$ and $\psi$ is equal to the number of coincidence points of $\wh\phi$ and $\wh\psi$ on the unitary dual, if the Reidemeister number is finite. An affirmative answer to the bitwisted Dehn conjugacy problem for almost polycyclic groups is obtained. Finally we explain why the Reidemeister numbers are always infinite for injective endomorphisms of Baumslag-Solitar groups.