On auto-nilpotent polygroups

The purpose of this paper is to introduce the concept of autonilpotent polygroups and investigate their properties concerning the automorphism of polygroups. To realize the article’s goals, we present the notation of m-very thin polygroups and construct the (non) commutative very thin polygroups on every (infinite) finite non–empty set, where m ∈ N. As a result of the research, is to show that the set of automorphism of some very thin polygroups is equal to the set of automorphism of special groups. The paper includes implications for the development of automorphism of polygroups, and shows that under some conditions very thin polygroups are autonilpotent polygroups and investigates the connection between of autonilpotent polygroups and nilpotent polygroups. The new conception of autonilpotent polygroups was broached for the in this paper the first time.