Equations in polyadic groups

Abstract

Systems of equations and their solution sets are studied in polyadic groups. We prove that a polyadic group $(G, f)=\mathrm{der}_{\theta, b}(G, \cdot)$ is equational noetherian, if and only if the ordinary group $(G, \cdot)$ is equational noetherian. The structure of coordinate polyadic group of algebraic sets in equational noetherian polyadic groups are also determined.