Original sentence: Equivalently, 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}.In mathematics, especially in the area of algebra known as group theory, a 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
Edited sentence: A Frobenius complement is a special type of complement in a Frobenius group.A p-complement is a complement to a Sylow p-subgroup.In mathematics, especially in the area of algebra known as group theory, a complement of a subgroup H in a group G is a subgroup K of G such that G = HK = { hk : h ∈ H and k ∈ K } and H ∩ K = {e}, that is, if every element of G has a unique expression as a product hk where h in H and k in K