Conjugacy growth in the higher Heisenberg groups

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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.
Original languageEnglish
JournalGlasgow Mathematical Journal
Publication statusPublished - 23 Jan 2023


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