We prove that a uniform pro-p group with no non-abelian free subgroups has a normal series with torsion-free abelian factors. We discuss this in relation to unique product groups. We also consider generalizations of Hantzsche–Wendt groups.

中文翻译：

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独特的产品组和全等子组

我们证明了一个统一的亲p没有非阿贝尔自由子群的群具有无扭阿贝尔因子的正态级数。我们讨论这个与独特的产品组有关的问题。我们还考虑 Hantzsche-Wendt 群的推广。