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2 results

  • 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.

  • The Conjugacy Ratio of Groups

  • Part of
  • Laura Ciobanu, Charles Garnet Cox, Armando Martino
  • Journal:
    Proceedings of the Edinburgh Mathematical Society / Volume 62 / Issue 3 / August 2019
    Published online by Cambridge University Press:
    22 February 2019, pp. 895-911
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  • In this paper we introduce and study the conjugacy ratio of a finitely generated group, which is the limit at infinity of the quotient of the conjugacy and standard growth functions. We conjecture that the conjugacy ratio is 0 for all groups except the virtually abelian ones, and confirm this conjecture for certain residually finite groups of subexponential growth, hyperbolic groups, right-angled Artin groups and the lamplighter group.