Solvable and nilpotent ultra-groups

We propose several characterizations of solvable ultra-groups and investigate the Jordan-Hölder Theorem and the Zassenhaus Lemma, in ultra-groups. We also define nilpotent ultra-groups by using the center of ultra-groups. Finally, we establish the relation between nilpotent and solvable ultra-groups. Our results aim to serve as a bridge between groups and ultra-groups.