Document Type : Research Paper

**Authors**

Department of Mathematics, Faculty of Physical Sciences, Ambrose Alli University, Ekpoma, Nigeria.

**Abstract**

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 $t\in A(Q)$.

**Keywords**

**Main Subjects**

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Available Online from 13 July 2022