International E-publication: Publish Projects, Dissertation, Theses, Books, Souvenir, Conference Proceeding with ISBN.  International E-Bulletin: Information/News regarding: Academics and Research

Discovery of New Classes of Ag-Groupoids

Author Affiliations

  • 1Department of Mathematics, Quad-i-Azam University, Islamabad, PAKISTAN
  • 2 Department of Mathematics, University of Malakand, PAKISTAN

Res. J. Recent Sci., Volume 1, Issue (11), Pages 47-49, November,2 (2012)


We discover eight new subclasses of AG-groupoids namely; anti-commutative AG-groupoid, transitively commutative AG-groupoid, self-dual AG-groupoid, unipotent AG-groupoid, left alternative AG-groupoid, right alternative AG-groupoid, alternative AG-groupoid and flexible AG-groupoid. We prove their existence by providing examples to these classes. We also prove some basic results of these classes and present a table of their enumeration up to order 6.


  1. Distler A., Shah M. and Sorge V., Enumeration of AG-groupoids, Lecture Notes in Computer Science, Volume 6824/2011, 1-14 (2011)
  2. GAP: Groups Algorithm and Programming, Version 4.4.12, 2008, (2012)
  3. Kazim M.A. and Naseerudin M., On almost semigroups, Portugaliae Mathematica.,36(1) (1977)
  4. Cho J.R., Pusan, Jezek J. and T. Kepka, Praha, Paramedial Groupoids, Czechoslovak Mathematical Journal, 49(124) (1996) Praha
  5. Stevanovic N. and Protic P.V., Abel-grassmann’s bands, Quasigroups and Related Systems,11(1), 95–101 (2004)
  6. Stevanovic N. and Protic P.V., Composition of Abel-Grassmann’s 3 -bands, Novi Sad J. Math., 34(2), 175-182 (2004)
  7. Naseeruddin M., Some studies on almost semigroups and flocks, PhD Thesis, The Aligarh Muslim University, India (1970)
  8. Shah M., A theoretical and computational investigations of AG-groups, PhD thesis, Quaid-i-Azam University Islamabad, (2012)
  9. Mushtaq Q. and Yusuf S.M., On Locally Associative LA-semigroup, J. Nat. Sci. Math., XIX(1), 57–62 (1979)
  10. Shah M., Shah T. and Ali A., On the cancellativity of AG-groupoids, International Mathematical Forum,6(44), 2187–2194 (2011)
  11. Howie J.M., Fundamentals of Semigroup Theory, Clarendon Press, Oxford, (2003)