SHONIBARE KAZEEM ADEKUNLE

Mathematics

At the Mathematics department office

Appointment on Visitation important

#	Certificate	School	Year
1.	M.Sc (Mathematics)	Department of Mathematics, Lagos State University	2017

Parastrophes of Inverse Property Loops

A loop is a quasigroup with a two sides identity. The parastrophe of a quasigroup G, . namely 12 -, 13 -, 23 -, 123 - and 132 - parastrophe are obtained by the exploit of left and right / divisions in G. This work investigates the relationship that exist between these parastrophes and their parent loops with respect to left inverse property L.I.P , right inverse property R.I.P , cross inverse property C.I.P and weak inverse property W.I.P loops. Our findings revealed that of the 5 parastrophes of L.I.P loop, 23 - parastrophe is a L.I.P loop, 12 - and 132 - parastrophes are R.I.P loop while 13 - and 132 - parastrophe are anti-automorphic inverse property loop. Similarly, 12 - and 132 - parastrophe of R.I.P loop are L.I.P loop , 13 -parastrophe of R.I.P is an R.I.P loop while 23 - and 123 - parastrophes are anti-automorphic inverse property loop. All the parastrophes of I.P loop are I.P loop. As for C.I.P loop, only 12 - parastrophe is a C.I.P loop, other parastrophes are symmetric loops of order 2. Finally, 12 -parastrophe of W.I.P loop is an I.P loop, 13 - , 23 - and 132 - parastrophes of W.I.P loop are C.I.P loop while 123 - parastrophe of W.I.P loop is a W.I.P loop with some of them true under minimal condition. Some of the results are new while some are extension of some existing results.

SHONIBARE KAZEEM is a Assistant Lecturer at the Department of Mathematics

SHONIBARE has a M.Sc in Mathematics from Department of Mathematics, Lagos State University