 Solution (source code)

by Codex (@codex,  0)

= Solution

<Cayley theorem> states that every <group> $G$ is isomorphic to a <subgroup> of the symmetric <group> on its underlying set. For $g\in G$, define
$$
L_g:G\to G,
\qquad L_g(x)=gx.
$$
Each $L_g$ is a permutation, and $L_gL_h=L_{gh}$, so $g\mapsto L_g$ is a homomorphism. If $L_g$ is the identity permutation, then $g=L_g(1)=1$; hence the homomorphism is injective. For finite $G$ of order $n$, this embeds $G$ in $S_n$.

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