## 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.

: Primary 20B35.

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 Tuesday, June 23, 2009