论文标题
不变的一代和花圈产品
Invariable generation and wreath products
论文作者
论文摘要
不变的生成是一个主要研究有限群体的主题。 2014年，Kantor，Lubotzky和Shalev生产了广泛的工具，用于调查无限群体的不变产生。自从他们的论文以来，各种作者已经调查了特定的无限群体或无限群体家庭的财产。 如果替换$ s $的每个元素，则一组由子集$ s $产生，其任何偶联物仍会导致$ g $的生成集。在本文中，我们研究了该特性在花圈产品方面的行为。我们的主要工作是处理$ g \ wr_x h $的基础的情况。我们在这里看到正面和负面的结果，具体取决于$ h $及其对$ x $的操作。
Invariable generation is a topic that has predominantly been studied for finite groups. In 2014, Kantor, Lubotzky, and Shalev produced extensive tools for investigating invariable generation for infinite groups. Since their paper, various authors have investigated the property for particular infinite groups or families of infinite groups. A group is invariably generated by a subset $S$ if replacing each element of $S$ with any of its conjugates still results in a generating set for $G$. In this paper we investigate how this property behaves with respect to wreath products. Our main work is to deal with the case where the base of $G\wr_X H$ is not invariably generated. We see both positive and negative results here depending on $H$ and its action on $X$.
