标题： 度量对称乘积的近似 显示英文标题

标题： Metric Approximations of Wreath Products

摘要： 鉴于已知的sofic群类很大，关于它们的保持性质的结果似乎存在不足。 我们针对Wreath积解决这个问题，并特别研究更一般的群度量逼近在Wreath积下的行为。 我们的主要结果如下。 假设$H$是一个sofic群，$G$是一个可数离散群。 如果$G$是sofic、超线性、弱sofic或线性sofic，那么$G\wr H$也分别是sofic、超线性、弱sofic或线性sofic。 在每种情况下，我们构造相关的度量逼近，扩展了用于$G\wr H$的一般度量逼近构造，该构造利用了$H$的sofic性。 显示英文摘要

摘要： Given the large class of groups already known to be sofic, there is seemingly a shortfall in results concerning their permanence properties. We address this problem for wreath products, and in particular investigate the behaviour of more general metric approximations of groups under wreath products. Our main result is the following. Suppose that $H$ is a sofic group and $G$ is a countable, discrete group. If $G$ is sofic, hyperlinear, weakly sofic, or linear sofic, then $G\wr H$ is also sofic, hyperlinear, weakly sofic, or linear sofic respectively. In each case we construct relevant metric approximations, extending a general construction of metric approximations for $G\wr H$ that uses soficity of $H$.