arXiv subjects
Publications and source records attributed to H. Khodabandeh.
Systems of equations and their solution sets are studied in polyadic groups. We prove that a polyadic group $(G, f)=\mathrm{der}_{θ, b}(G, \cdot)$ 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.
The main aim of this article is to establish a classification of simple polyadic groups in terms of ordinary groups and their automorphisms. We give two different definitions of simpleness for polyadic groups, from the point of views of universal algebra, UAS (universal algebraically simpleness), and group theory, GTS (group theoretically simpleness). We obtain the necessary and sufficient conditions for a polyadic group to be UAS or GTS.