Definition with symbols
Let be groups. A map is termed a bihomomorphism if for every in , the induced map is a homomorphism from to , and for every , the induced map is a homomorphism from to .
Bihomomorphism is a group-theoretic variant of the notion of bilinear map in vector spaces.
- Subgroup generated by image of bihomomorphism is abelian, or in other words, all the elements that can be written as images under the bihomomorphisms commute with each other.
- Kernel of a bihomomorphism implies abelian-quotient, follows from the preceding.
- Kernel of a bihomomorphism implies completely divisibility-closed