(i) | ${\leq}$ is a D2192: Subgroup relation on $G$ |

(ii) | $E \subseteq G$ is a D78: Subset of $G$ |

**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}