Magma Proof of Strict Inequalities for Minimal Degrees of Finite Groups

The minimal faithful permutation degree of a finite group $G$, denote by $\mu (G)$ is the least non-negative integer $n$ such that $G$ embeds inside the symmetric group $\text{Sym}(n)$. In this paper, we outline a Magma proof that 10 is the smallest degree for which there are groups $G$ and $H$ such that $\mu(G \times H) < \mu(G)+ \mu(H)$.