关于具有有限正则文件基的无挠的群
On torsion-free groups with finite regular file bases
摘要：
1995年，V.V. Bludov在The Kourovka Notebook中提出了以下问题：如果一个无挠的群$G$有一个有限的生成元系统$a_1$，.，$a_n$，使得$G$的每个元素都以$a_1^{k_1}... a_n^{k_n}$的形式具有独特的呈现，其中$k_i\in\mathbb Z$，$G$实际上是多环的吗？答案是“不总是。本文构造了一个由生成元和定义关系表示的群的反例。
英文摘要：
The following question was asked by V. V. Bludov in The Kourovka Notebook in 1995: If a torsion-free group $G$ has a finite system of generators $a_1$, ..., $a_n$ such that every element of $G$ has a unique presentation in the form $a_1^{k_1}... a_n^{k_n}$ where $k_i\in\mathbb Z$, is it true that $G$ is virtually polycyclic? The answer is ``not always.'' A counterexample is constructed in this paper as a group presented by generators and defining relations.
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