Definition:Complement of Subgroup/Definition 2

Definition

Let $G$ be a group with identity $e$.

Let $H$ and $K$ be subgroups of $G$.

Let $H K$ be their subset product and $H \cap K$ their intersection.

$K$ is a complement of $H$ if and only if:

$G = K H$ and $H \cap K = \set e$

Also see

• Equivalence of Definitions of Complement of Subgroup