A Theoretical and Computational Investigation of AG-groups

ISBN-13: 9783659840401 / Angielski / Miękka / 2016 / 204 str.

Muhammad Shah

Opis

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.

O autorze

Author Profile:Dr. Muhammad Shah did his M.Sc from University Of Peshawar in 1998. He did his PhD in 2012 from Quaid-i-Azam University Islamabad in computational Algebra. In 2010, he was awarded IRSIP scholarship of HEC for Birmingham University UK. HEC has kept his research papers' record on its site in Success Story for so long.