# Category:Definitions/Subgroup Complements

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This category contains definitions related to Subgroup Complements.

Related results can be found in Category:Subgroup Complements.

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.

### Definition 1

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

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

### Definition 2

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

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

## Pages in category "Definitions/Subgroup Complements"

The following 3 pages are in this category, out of 3 total.