Subgroups
Definition
If all of the following are true:
$(H, \cdot_H)$ and $(G, \cdot_G)$ are both groups
$H \subseteq G$
$h_1 \cdot_H h_2 = h_1 \cdot_G h_2$ for every $h_1, h_2 \in H$
then we say that $H$ is a subgroup of $G$.

Referenced by: