Magma Proof of Strict Inequalities for Minimal Degrees of Finite Groups

Scott H. Murray and Neil Saunders

Abstract

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

Keywords: Faithful Permutation Representations.

AMS Subject Classification: Primary 20B35.