It is shown that there is a finitely generated metabelian group of finite torsion-free rank associated with each non-constant integer polynomial. It is shown how many structural properties of the group can be detected by inspecting the polynomial.

中文翻译：

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由整数多项式产生的有限生成元贝尔群

结果表明，存在与每个非常数整数多项式相关联的有限生成的有限无扭秩元贝尔群。它显示了通过检查多项式可以检测到群的多少结构属性。