Constructions and involutory properties in latin quandles

This work studied involutory properties in Latin quandles using methods of quasiqroup theory, and classified latin quandle Q into Left Involutory Property latin Quandle (LIPQ), Right Involutory Property Latin Quandle (RIPQ) and Involutory Property Latin Quandle (IPQ). It investigated a fourth property called the Cross Involutory Property Latin Quandle (CIPQ). The result showed that a latin quandle Q that is a LIPQ and RIPQ is an IPQ. Moreover, it established that the necessary and sufficient conditions for a latin Alexander quandle Q to be a CIPQ is that b=t^۲a +(۱-t)(tb+a) for all a,b \in Q and t\in A(Q).

Keywords:

Latin quandles , LIPQ , RIPQ , CIPQ , IPQ