Multiplicity-free tensor products of irreducible modules over simple algebraic groups in positive characteristic

Let $k$ be an algebraically closed field of characteristic $p>0$. In this master thesis, we classify multiplicity-free tensor products of simple modules for the groups $S{L}_2(k)$ and $S{L}_3(k)$. We also provide a classification for $S{L}_n(k)$ when $p=2$ and give partial results in the case of $S{p}_4(k)$.