Some properties of finite generalized-groups

In this article, we discuss  the concept of completely simple-semigroups, which serves as a natural extension of the group structures. These semigroups, also known as generalized-groups, provide an interesting generalization beyond the realm of the groups. Many scientists have investigated various applications of generalized-groups. Notably, this algebraic structure has connections to the unified gauge theory. In this article, we investigate the structures and properties of generalized-groups, providing examples and results within this fascinating subject. Specially, we show that the generalized Lagrange Theorem may not be true for generalized-groups.