\begin{definition}[Definition:Generated Algebraic Substructure]
Let $\struct {A, \circ}$ be an algebraic structure.
Let $G \subseteq A$ be any subset of $A$.
The '''algebraic substructure generated''' by $G$ is the smallest substructure of $\struct {A, \circ}$ which contains $G$.
It is written $\gen G$.
\end{definition}