论文标题
有限生成的阿贝尔组的花圈产品的边界共轭深度功能
Bounding conjugacy depth functions for wreath products of finitely generated abelian groups
论文作者
论文摘要
在本文中，我们研究了亚伯群的花环产品的共轭可分离性的渐近行为。我们在灯泡组的情况下充分表征了渐近类，并为广义灯泡组提供了指数上限和下限。在基本组无限的情况下，我们给出了上下边界。我们将结果应用于获得的下限，以供其群体的各种环形产品的共轭深度函数，而该群体不是Abelian。
In this article, we study the asymptotic behaviour of conjugacy separability for wreath products of abelian groups. We fully characterise the asymptotic class in the case of lamplighter groups and give exponential upper and lower bounds for generalised lamplighter groups. In the case where the base group is infinite, we give superexponential lower and upper bounds. We apply our results to obtain lower bounds for conjugacy depth functions of various wreath products of groups where the acting group is not abelian.
