高海森堡群的共轭增长

IF 0.5 4区数学 Q3 MATHEMATICS

Glasgow Mathematical Journal Pub Date : 2021-11-11 DOI:10.1017/S0017089522000428

Alex Evetts

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引用次数: 2

摘要

摘要我们计算了有限生成的第2类幂零群的共轭增长函数的渐近估计，这些群的导出子群是无限循环的，包括所谓的高海森堡群。我们通过理解它们的扭曲共轭增长，证明了这些渐近性在传递到可公度群时是稳定的。我们还用这些估计来证明，在某些情况下，共轭增长序列不可能是完整函数。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Conjugacy growth in the higher Heisenberg groups

Abstract 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.

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来源期刊

Glasgow Mathematical Journal 数学-数学

CiteScore

1.10

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Glasgow Mathematical Journal publishes original research papers in any branch of pure and applied mathematics. An international journal, its policy is to feature a wide variety of research areas, which in recent issues have included ring theory, group theory, functional analysis, combinatorics, differential equations, differential geometry, number theory, algebraic topology, and the application of such methods in applied mathematics. The journal has a web-based submission system for articles. For details of how to to upload your paper see GMJ - Online Submission Guidelines or go directly to the submission site.