Let $G$ be a D22: Group such that

(i)	${\leq}$ is a D2192: Subgroup relation on $G$
(ii)	$E \subseteq G$ is a D78: Subset of $G$

The generated subgroup of $G$ with generator $E$ is the D11: Set \begin{equation} \langle E \rangle : = \bigcap \{ H : E \subseteq H \leq G \} \end{equation}