Equational Noethericity of Metabelian r -Groups

[摘要] 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.

[学科分类] 数学（综合）

[关键词] metabelian group;divisible group;equationally Noetherian group