On the finite Loop Algebra of the smallest Moufang loop $M(S_3,2)$

Abstract

Let $F[L]$ be a loop algebra of a loop $L$ over a field $F$. In this paper, we obtain the unit loop of the loop algebra $F[L],$ where $L$ is the smallest Moufang loop $M(S_3,2)$ and $F$ is a finite field of characteristic different from $3$.