Complement (group theory)

In group theory, the complement of a subgroup $H$ in a group $G$ is a subgroup $K$ of $G$ such that $H$ and $K$ together generate $G$ and the intersection of $H$ and $K$ is the identity: let $H$ be a subgroup of the group $G$. A subgroup $K$ of $G$ is called a complement for $H$ in $G$ if Failed to parse (syntax error): {\displaystyle G = HK = { hk | h \in H & k \in K }} and $H$ ∩ $K={e}$.

Reference

• David S. Dummit & Richard M. Foote (2003). Abstract Algebra. Wiley. ISBN 978-0-471-43334-7.