Definition:Subgroup

Definition
Let $\struct {G, \circ}$ be an algebraic structure.

$\struct {H, \circ}$ is a subgroup of $\struct {G, \circ}$ :


 * $(1): \quad \struct {H, \circ}$ is a group
 * $(2): \quad H$ is a subset of $G$.

This is represented symbolically as $H \le G$.

It is usual that $\struct {G, \circ}$ is itself a group, but that is not necessary for the definition.

Also see

 * One-Step Subgroup Test
 * Two-Step Subgroup Test
 * Finite Subgroup Test