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Fundamentalnaya i Prikladnaya Matematika, 2016, Volume 21, Issue 5, Pages 219–227 (Mi fpm1765)  

This article is cited in 2 scientific papers (total in 2 papers)

Two examples related to the twisted Burnside–Frobenius theory for infinitely generated groups

E. V. Troitskii

Moscow State University, Moscow, Russia
Full-text PDF (146 kB) Citations (2)
References:
Abstract: The TBFT$_f$ conjecture, which is a modification of a conjecture by Fel'shtyn and Hill, says that if the Reidemeister number $R(\phi)$ of an automorphism $\phi$ of a (countable discrete) group $G$ is finite, then it coincides with the number of fixed points of the corresponding homeomorphism $\hat{\phi}$ of $\hat{G}_f$ (the part of the unitary dual formed by finite-dimensional representations). The study of this problem for residually finite groups has been the subject of some recent activity. We prove here that for infinitely generated residually finite groups there are positive and negative examples for this conjecture. It is detected that the finiteness properties of the number of fixed points of $\phi$ itself also differ from the finitely generated case.
Funding agency Grant number
Russian Science Foundation 16-11-10018
This work was supported by the Russian Science Foundation under grant 16-11-10018.
English version:
Journal of Mathematical Sciences (New York), 2020, Volume 248, Issue 5, Pages 661–666
DOI: https://doi.org/10.1007/s10958-020-04903-0
Document Type: Article
UDC: 512.547.4+517.986.66
Language: Russian
Citation: E. V. Troitskii, “Two examples related to the twisted Burnside–Frobenius theory for infinitely generated groups”, Fundam. Prikl. Mat., 21:5 (2016), 219–227; J. Math. Sci., 248:5 (2020), 661–666
Citation in format AMSBIB
\Bibitem{Tro16}
\by E.~V.~Troitskii
\paper Two examples related to the twisted Burnside--Frobenius theory for infinitely generated groups
\jour Fundam. Prikl. Mat.
\yr 2016
\vol 21
\issue 5
\pages 219--227
\mathnet{http://mi.mathnet.ru/fpm1765}
\transl
\jour J. Math. Sci.
\yr 2020
\vol 248
\issue 5
\pages 661--666
\crossref{https://doi.org/10.1007/s10958-020-04903-0}
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  • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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