论文标题
产品品种中的凝结组
Condensed groups in product varieties
论文作者
论文摘要
据说有限生成的$ g $如果其在有限生成的标记组空间中的同构类别没有隔离点，则可以凝结。我们证明，每个产品品种$ \ Mathcal {uv} $，其中$ \ Mathcal {u} $（分别是$ \ Mathcal {V} $）是一个非亚伯利亚（分别是非局部的）品种，包含一个浓缩的组。特别是，存在有限指数的凝结组。作为一个应用程序，我们在$ \ Mathcal {uv} $中的一组有限生成的组中获得了同构关系的结构和基本等价的结构。
A finitely generated group $G$ is said to be condensed if its isomorphism class in the space of finitely generated marked groups has no isolated points. We prove that every product variety $\mathcal{UV}$, where $\mathcal{U}$ (respectively, $\mathcal{V}$) is a non-abelian (respectively, a non-locally-finite) variety, contains a condensed group. In particular, there exist condensed groups of finite exponent. As an application, we obtain some results on the structure of the isomorphism relation and elementary equivalence on the set of finitely generated groups in $\mathcal{UV}$.
