# Cayley's Theorem…

Let G be a group. For $g \in G$ write $l_g : G \rightarrow G$ for the function $l_g(g') = gg'$. Then $l_g$ is a permutation of G. Moveover, if we define $\Lambda: G \rightarrow S(G)$ by $\Lambda(g) = l_g$, then $\Lambda$ is an embedding. In consequence, if G is finite, then it is isomorphic to a subgroup of $S_{|G|}$.

My question:

What does "embedding" mean? Does it have a formal definition, or does it just mean a function that is not surjective? I tried to search the definition online but couldn't find anything useful.

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In this case, embedding is being used to say that $G$ has a copy of itself into $S(G)$, that is, there exists an injective homomorphism onto its image.