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Twisted Burnside Theorem for Two-step Torsion-free Nilpotent Groups

  • Alexander Fel’shtyn
  • Fedor Indukaev
  • Evgenij Troitsky
Part of the Trends in Mathematics book series (TM)

Abstract

It is proved that the Reidemeister number of any automorphism of any finitely generated torsion-free two-step nilpotent group coincides with the number of fixed points of the corresponding homeomorphism of the finited-imensional part of the dual space (of equivalence classes of unitary representations) provided that at least one of these numbers is finite. An important example of the discrete Heisenberg group is studied in detail.

Keywords

Reidemeister number twisted conjugacy classes Burnside theorem two-step nilpotent group Heisenberg group 

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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2008

Authors and Affiliations

  • Alexander Fel’shtyn
    • 1
  • Fedor Indukaev
    • 2
  • Evgenij Troitsky
    • 2
  1. 1.Instytut MatematykiUniwersytet SzczecinskiSzczecinPoland
  2. 2.Dept. of Mech. and Math.Moscow State UniversityMoscowRussia

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