Bitwisted Burnside-Frobenius theorem and Dehn conjugacy problem
Volume 85 / 2009
Banach Center Publications 85 (2009), 31-42
MSC: 20C, 20E45, 22D10, 22D25, 37C25, 43A30, 46L, 47H10, 54H25, 55M20.
DOI: 10.4064/bc85-0-2
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 $\widehat\phi$ and $\widehat\psi$ 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.
