Definition:Complement of Subgroup

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

Let $H$ and $K$ be subgroups.

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

Also known as
If $H$ is a complement of $K$ (and thus equivalently, if $K$ is a complement of $H$) the subgroups are said to be complementary.

Also see

 * Equivalence of Definitions of Complement of Subgroup