On autosolvable and autonilpotent polygroups

Polygroups are another important class of hypergroups. The importance of polygroups is their connection to graphs, relations and Boolean algebras. In this paper, we study notions of autosolvable and autonilpotent polygroups by using the heart of a polygroup. This study introduces the concept of autosolvable and autonilpotent polygroups with respect to the automorphism of polygroups. We also prove that autonilpotent polygroups are autosolvable.