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.

中文翻译：

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高阶海森堡群中的共轭增长

我们计算有限生成的第 2 类幂零群的共轭增长函数的渐近估计，其派生子群是无限循环的，包括所谓的高等海森堡群。我们通过了解它们扭曲的共轭增长，证明这些渐近线在传递给可公度群时是稳定的。我们还使用这些估计来证明，在某些情况下，共轭增长序列不可能是完整函数。