Subgroup

A subset H of a group (G,$\cdot$) is called a subgroup, if (H,$\cdot$) is itself a group.

Simple Examples

1. $(2\mathbb {Z} ,+)$ is a subgroup of $(\mathbb {Z} ,+)$
2. $(\mathbb {Z} ,+)$ is a subgroup of $(\mathbb {Q} ,+)$
3. $(\mathbb {Q} ^{+},\cdot )$ is a subgroup of $(\mathbb {R} ^{+},\cdot )$