subgroup

Definition

A subset $H \subseteq G$ is a subgroup of group $G$ if the following properties hold:

• closure, if $a \in H$, $b\in H$, then $ab \in H$
• identity, $1 \in H$
• inverses, if $a \in H$, then $a^{-1}\in H$

References

1. M. Artin, Algebra, 2. ed. Boston, Mass. Munich: Pearson Education, Prentice Hall, 2011, p. 42.