群的渐近增长与最小公倍数
Asymptotic growth and least common multiples in groups
摘要：
在本文中，我们将词和子群增长与剩余有限性量化中出现的某些函数联系起来。这种努力的一个结果是一对结果，等同于一个有限生成群的幂零性与这些功能的渐近行为。本文的后半部分研究了其中两个函数的渐近行为。我们的主要结果在这个舞台上解决了一个问题的Bogopolski从Kourovka笔记本关于下界这些功能之一的nonabelian自由群。
英文摘要：
In this article we relate word and subgroup growth to certain functions that arise in the quantification of residual finiteness. One consequence of this endeavor is a pair of results that equate the nilpotency of a finitely generated group with the asymptotic behavior of these functions. The second half of this article investigates the asymptotic behavior of two of these functions. Our main result in this arena resolves a question of Bogopolski from the Kourovka notebook concerning lower bounds of one of these functions for nonabelian free groups.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
