On nilpotent and solvable polygroups

Abstract

Applications of hypergroups have mainly appeared in special subclasses. One of the important subclasses is the class of polygroups. <br /> In this paper, we study the notions of nilpotent and solvable polygroups by using the notion of heart of polygroups. In particular, we give <br /> a necessary and sufficient condition between nilpotent (solvable) polygroups and fundamental groups.