It is proved for Abelian groups that the Reidemeister coincidence number of two endomorphisms ϕ and ψ is equal to the number of coincidence points of ϕ̂ and ψ̂ 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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc85-0-2,
author = {Alexander Fel'shtyn},
title = {Bitwisted Burnside-Frobenius theorem and Dehn conjugacy problem},
journal = {Banach Center Publications},
volume = {86},
year = {2009},
pages = {31-42},
zbl = {1203.22007},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc85-0-2}
}
Alexander Fel'shtyn. Bitwisted Burnside-Frobenius theorem and Dehn conjugacy problem. Banach Center Publications, Tome 86 (2009) pp. 31-42. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc85-0-2/