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

Troitsky, E. V. (2020). Two examples related to the twisted Burnside-Frobenius theory for infinitely generated groups. Journal of Mathematical Sciences, 248(5), 661-666. doi:10.1007/s10958-020-04903-0.

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Troitsky_Two Examples Related to the Twisted Burnside–Frobenius Theory for Infinitely Generated Groups_2020.pdf (Publisher version), 160KB
 
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Troitsky_Two Examples Related to the Twisted Burnside–Frobenius Theory for Infinitely Generated Groups_2020.pdf
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https://doi.org/10.1007/s10958-020-04903-0 (Publisher version)
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Troitsky, E. V.1, Author           
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1Max Planck Institute for Mathematics, Max Planck Society, ou_3029201              

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 Abstract: The TBFTf conjecture, which is a modification of a conjecture by Fel’shtyn and Hill, says that
if the Reidemeister number R(φ) of an automorphism φ of a (countable discrete) group G is finite, then it
coincides with the number of fixed points of the corresponding homeomorphism φˆ of Gˆf (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 φ itself also differ from the finitely generated case.

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Language(s): eng - English
 Dates: 2020
 Publication Status: Issued
 Pages: 6
 Publishing info: -
 Table of Contents: -
 Rev. Type: Peer
 Identifiers: DOI: 10.1007/s10958-020-04903-0
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Title: Journal of Mathematical Sciences
  Abbreviation : J. Math. Sci.
Source Genre: Journal
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Publ. Info: Springer
Pages: - Volume / Issue: 248 (5) Sequence Number: - Start / End Page: 661 - 666 Identifier: ISSN: 1573-8795