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2 results

  • The Reidemeister spectrum of finite abelian groups

  • Part of
  • Pieter Senden
  • Journal:
    Proceedings of the Edinburgh Mathematical Society / Volume 66 / Issue 4 / November 2023
    Published online by Cambridge University Press:
    06 September 2023, pp. 940-959
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  • For a finite abelian group A, the Reidemeister number of an endomorphism φ is the same as the number of fixed points of φ, and the Reidemeister spectrum of A is completely determined by the Reidemeister spectra of its Sylow p-subgroups. To compute the Reidemeister spectrum of a finite abelian p-group P, we introduce a new number associated to an automorphism ψ of P that captures the number of fixed points of ψ and its (additive) multiples, we provide upper and lower bounds for that number, and we prove that every power of p between those bounds occurs as such a number.

  • Conjugacy growth in the higher Heisenberg groups

  • Part of
  • Alex Evetts
  • Journal:
    Glasgow Mathematical Journal / Volume 65 / Issue S1 / May 2023
    Published online by Cambridge University Press:
    23 January 2023, pp. S148-S169
    Print publication:
    May 2023
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  • We calculate asymptotic estimates for the conjugacy growth function of finitely generated class 2 nilpotent groups whose derived subgroups are infinite cyclic, including the so-called higher Heisenberg groups. We prove that these asymptotics are stable when passing to commensurable groups, by understanding their twisted conjugacy growth. We also use these estimates to prove that, in certain cases, the conjugacy growth series cannot be a holonomic function.