INSTITUTE OF MATHEMATICS · POLISH ACADEMY OF SCIENCES BANACH CENTER PUBLICATIONS ISSN: 0137-6934(p) 1730-6299(e)

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Bitwisted Burnside-Frobenius theorem and Dehn conjugacy problem

Alexander Fel'shtyn¹
Banach Center Publ. 85 (2009), 31-42
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.

MSC (2010): 20C, 20E45, 22D10, 22D25, 37C25, 43A30, 46L, 47H10, 54H25, 55M20.
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1. Instytut Matematyki
   Uniwersytet Szczeciński
   ul. Wielkopolska 15
   70-451 Szczecin, Poland
   and
   Boise State University
   1910 University Drive
   Boise, ID 83725-155, USA
   

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