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 G = HK = { hk : h ∈ H & k ∈ K } and H ∩ K = {e}.

Reference

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