Definition:Complement of Subgroup/Definition 1

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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:

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


Also see


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