Abstract 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≀XHG\wr_{X}H is not invariably generated. We see both positive and negative results here depending on 𝐻 and its action on 𝑋.

中文翻译：

---

不变代和花圈产品

摘要 不变生成是一个主要针对有限群研究的主题。2014 年，Kantor、Lubotzky 和 ​​Shalev 开发了广泛的工具来研究无限群的不变生成。自从他们发表论文以来，许多作者已经研究了特定无限群或无限群族的性质。如果用它的任何共轭替换𝑆的每个元素仍然会产生𝐺的生成集，则一个组总是由子集𝑆生成。在本文中，我们研究了此属性在花圈产品方面的表现。我们的主要工作是处理 G≀XHG\wr_{X}H 的基不是总是生成的情况。我们在这里看到了正面和负面的结果，这取决于 𝐻 及其对 𝑋 的作用。