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Bitwisted Burnside-Frobenius theorem and Dehn conjugacy problem

Tom 85 / 2009

Alexander Fel'shtyn Banach Center Publications 85 (2009), 31-42 MSC: 20C, 20E45, 22D10, 22D25, 37C25, 43A30, 46L, 47H10, 54H25, 55M20. DOI: 10.4064/bc85-0-2

Streszczenie

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.

Autorzy

  • Alexander Fel'shtynInstytut Matematyki
    Uniwersytet Szczeciński
    ul. Wielkopolska 15
    70-451 Szczecin, Poland
    and
    Boise State University
    1910 University Drive
    Boise, ID 83725-155, USA
    e-mail

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