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.