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 $b=t^2a +(1-t)(tb+a)$ for all $a,b in q$ and $tin a(q)$.