The author had earlier defined the concept of an r-group, generalizing the concept of a rigid (solvable) group. This article proves that every metabelian r-group is equationally Noetherian; i.e., each system of equations in finitely many variables with coefficients in the group is equivalent to some finite subsystem.

中文翻译：

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Metabelian r-群的等式非以太性

作者早先定义了 r 群的概念，概括了刚性（可解）群的概念。这篇文章证明了每个metabelian r-group 都是等式的Noetherian；即，在群中具有系数的有限多个变量中的每个方程组等价于某个有限子系统。