It is proved that there exist uncountably many nonisomorphic pro-p-groups admitting presentations with two generating elements and one defining relation in the variety of metabelian pro-p-groups. Also we give information on pro-p-groups with a single relation in varieties of nilpotent pro-p-groups.

中文翻译：

---

具有单一关系的 Metabelian Pro-p-Groups

证明了在各种metabelian pro-p-群中存在着无数的非同构pro-p-群承认具有两个生成元素和一个定义关系的表示。我们还提供了关于在各种幂零 pro-p-groups 中具有单一关系的 pro-p-groups 的信息。