Kernel of a multihomomorphism implies completely divisibility-closed
Suppose and are groups, and:
(where the occurs times) is a multihomomorphism. Define:
Then, is a completely divisibility-closed subgroup of .
- Kernel of a multihomomorphism implies intersection of kernels of bihomomorphisms
- Intersection of kernels of bihomomorphisms implies completely divisibility-closed
The proof follows by combining Facts (1) and (2).