Abstract. Using a unified method, we determine the structure of automorphisms and representations of arbitrary polyadic groups. More precisely, for a polyadic group (G, f ) = der θ,b (G, ·), we obtain a complete description of automorphisms and representations of (G, f ) in terms of automorphisms and representations of the binary group (G, ·).
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.
Abstract. Systems of equations and their solution sets are studied in polyadic groups. We prove that a polyadic group (G, f ) = der θ,b (G, ·) is equational noetherian, if and only if the ordinary group (G, ·) is equational noetherian. The structure of coordinate polyadic group of algebraic sets in equational noetherian polyadic groups are also determined.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.