Applications of the gamma*-relation to polygroups

The gamma*-relation was introduced by Freni. In this article, we use the gamma*-relation in a given polygroup. In this way, the gamma*-relation is the smallest equivalence relation on a polygroup P such that P/gamma* is an abelian group. Results are obtained on extension polygroups, derived hypergroups, gamma-parts, and semi-direct hyperproduct.