A Theoretical and Computational Investigation of AG-groups

Achievements of the study: This is the first survey of AG-groupoids. Enumeration and classi_cation of AG-groupoids up to order 6. Enumeration of AG-monoids up to order 8. Computational enumeration of AG-groups up to order 12. Algebraic enumeration of AG-groups of every order n. Enumeration of Jordan loops up to order 9. Proving that C-loops of certain order do not exist. Discovery of at least 24 new classes of AG-groupoids. Discovery of a new class of groupoid which we call Bol* groupoid. Discovery of a new class of semigroup which we call AG-groupoid semigroup. of a new class of quasigroup which we ca1Discovery ll Bol* quasigroup and which is a generalization of AG-group. Burmistrovich's theorem for AG-groupoids. Construction of AG-groups, AG-monoids and Jordan loops to obtain them manually. We de_ned Smarandache AG-group. We studied AG-group as a generalization of abelian group. We studied AG-group as a generalization of loop and as quasigroup. We studied AG-group as a subclass of right Bol quasigroup. We studied Multiplication group and inner mapping group of AG-group. We did a sort of application of AG-groups in geometry. A GAP Package, AGGROUPOID CONSTRUCTED.