An Introduction to Ω-Subgroup

Abstract

In the language of Ω-groupoid we introduce Ω-subgroup, where a groupoid is an algebraic structure endow with one binary operation. Ω-subgroup is defined, as a generalization of the classical subgroup. In this case it was shown that the properties of Ω-groups are inherent in their Ω-subgroups. We then introduce and define the notions: center of an Ω-group, centralizers and normalizers of an Ω-subset of an Ω-group. Furthermore we investigate and prove some of the properties of these notions as in the case of classical group theory.