I was born in the city of Abeokuta, Ogun State in Nigeria. I had my Nursery and Primary School Educations at the Children House School, Ibara, Abeokuta, Ogun State, Nigeria, from 1983 to 1989. My Junior and Secoundary School education were at the Baptist Boys' High School, Oke-Saje, Abeokuta, Ogun State, Nigeria, between 1990 and 1996. I got a B.Sc. degree in Mathematical Science (with bias in Mathematics) in 2002, M.Sc. degree in Mathematics  in 2005 and Ph.D. degree in Mathematics in 2009 at the University of Agriculture, Abeokuta, Nigeria (now Federal University of Agriculture, Abeokuta, Nigeria). My M.Sc. and Ph.D. theses were based on the notions of "Central Loops" and "Osborn Loops" in the field of Algebra known as "Theory of Quasigroups and Loops". I have been doing research in the field of "Theory of Quasigroups and Loops" for the past  13 years and has  not  less than 50 research articles published in international and reputable journals. After my graduate studies at the University of Agriculture, Abeokuta, I got an appointment at the Department of Mathematics, Faculty of Science, Obafemi Awolowo University (OAU), Ile-Ife, Nigeria as an Assistant Lecturer and I have since risen to the postition of a Lecturer I. Since my assumption of duty at OAU, I have been teaching Algebra courses at undegraduate and post graduate levels, I have supervised an M.Sc. Mathematics thesis and I am presently supervising a Ph.D. Mathematics thesis. I have served as a member of some academic and administrative commitees both in the Department, Faculty and the University. I have attended national and International Conferences and Schools.  I am married to Mrs. Oluwaseun Jaiyeola.


1.         Groupoid, Quasigroup and Loop Theory:

a.         Osborn Loops-The Universality of Osborn Loops was an open problem proposed by Michael K. Kinyon in a talk titled “A survey of Osborn loops” which he gave in 2005 at the Milehigh conference on loops, quasigroups and non-associative systems, University of Denver, Denver, Colorado, USA. The solution to this problem was the main focus of my Ph. D. work. I am presently working on the answers to some of the questions attached to the open problem. Like:

i.          Does there exist a nice identity that characterizes a universal Osborn loop?

ii.         Does there exist a proper Osborn with a trivial nucleus?

iii         Conjecture: Are all CC-quasigroups isotopic to a Osborn loop?

 b.         Weak Inverse Property Loops and Its Generalizations-Karklinush and Karklin have generalized the study of WIPLs and CIPLs to the study of m-inverse loops and (r,s,t)-inverse loops.  After the study of m-inverse loops by Keedwell and Shcherbacov, they have also generalized them to quasigroups called (r,s,t)-inverse quasigroups. It  is of interesting to me to study the universality of m-inverse loops, (r,s,t)-inverse quasigroups and (α,β,γ)-inverse quasigroups. These will generalize the works of J. M. Osborn and R. Artzy on universal WIPLs and CIPLs respectively.

 c.        Groupoid and Quasigroups generated by linear-bivariate polynomial p(x,y)=a+bx+cy over the ring   -Groupoids and quasigroups generated by p(x,y)=a+bx+cy have been cited as example for few varieties of groupoid and quasigroups in the past. I am currently supervising an M.Sc. work which:

  1. studies the characterization of some varieties of groupoids and quasigroups which are generated by p(x,y)=a+bx+cy over the ring.
    1. investigates the existence of a group of  linear-bivariate polynomials that generate quasigroups over the ring   .
    2. introduces and studies the right, left and middle linear-bivariate polynomials of a linear-bivariate polynomial that generates a quasigroup over the ring.

d.         Buchsteiner Loops-I am investigating the relationship between Buchsteiner loops and Osborn loops.

e.         Construction of Nested Balanced Incomplete Block Designs-I am presently working in conjunction with Mr. Saka on the possibility of  using quasigroups, loops and latin squares to construct Nested Balanced Incomplete Block Designs (NBIBD). Our attention is been called to SUDOKU.

 2.         Smarandache Quasigroup and Loop Theory:

a.          Theory of Smarandache Loops: Am introducing more Smarandache concepts (apart from thoserecently introduced by W. B. Vasantha Kandasamy in 2002) into loops and quasigroups and also studying them. In 2007, A. S. Muktibodh the Head of the Department of Mathematics in Mohota Science College, Nagpur India.contacted me and invited me to contribute to his project title “Smarandache Algebraic Structures”. In 2008, A. Balu, a Research Associate of Alagappa University, Karaikudi, India who presently works  on Quasigroup based cryptosystem contacted me for a possible collaborative work.

b.          Theory of Smarandache Bol Loops: Am presently developing the Theory of 2nd Smarandache Bol loops. Dr. Arun S. Muktibodh, an Associate Professor and HOD Mathematics, Mohota College of Science, Nagpur, India has shown interest in the construction of a 2nd Smarandache Bol loop that is not a Bol loop.

3.         Number Theory:Palindromes and Generalised Smarandache Palindromes.

The challenge of counting the number of palindromes and generalized Smarandache palindromes is still on. I have started studying these by the use of palindromic permutation. I have been able look at the  palindromic permutations and generalized Smarandache palindromic permutations of the symnmetric groups of degrese 2 and 3. Mr. Olurode has joined me in this work and he is counting the palindromic permutations and generalized Smarandache palindromic permutations of the symnmetric groups of degrees 4 and 5.

4.      Cryptography: This is the science of securing of message which is to be sent through an insecured medium to an intended receiver such that the original message would not be known to any external party. Am still in the search of more identities that are true in universal Osborn loops which would be useful for cryptography. The further applications of (r,s,t)-inverse quasigroups and (α,β,γ)-inverse quasigroups to cryptography is still of interest to me. I have a strong believe that groupoids and quasigroups generated by p(x,y)=a+bx+cy will be of double advantage for cryptography because of their non-associative structure and the fact that their formulation is based on integers.

5.      Algebras: BCC-algebra, BCI-algebra, BCK-algebra, Hilbert-algebra, AC-algebras.

I and Mr. Emmanuel Ilojide of the Federal University of Agriculture, Abeokuta, Nigeria, are presently generalizing the aforementioned algebras, especially BCI-algebra and BCK-algebra which were introduced by Imai, K. Iséki and S. Tanaka in 1966. We are also studying the algebraic properties of Non-associative/Bol-Moufang type/Fenyves BCI-algebras.

6.      Combinatorial Statistics: Nested Balanced Incomplete Block Design (NBIBD) of Resolvable Type-I am presently collaborating with Mr. Saka on the use of algebraic procedures, algebraic structures like groups, quasigroups and loops and combinatorial structures like latin squares and SUDUKO squares in the construction of NBIBD of Resolvable Type.