\begin{definition}[Definition:Group Presentation]
Let $G$ be a group.
A '''presentation for $G$''' is a triple $\tuple {S, R, f}$ where:
:$S$ is a set
:$R$ is a set of relations on $S$
:$f: \gen {S \mid R} \to G$ is a group isomorphism from the group defined by $\struct {S, R}$.
\end{definition}