Intersection of kernels of bihomomorphisms implies completely divisibility-closed

From Groupprops
Jump to: navigation, search
This article gives the statement and possibly, proof, of an implication relation between two subgroup properties. That is, it states that every subgroup satisfying the first subgroup property (i.e., intersection of kernels of bihomomorphisms) must also satisfy the second subgroup property (i.e., completely divisibility-closed subgroup)
View all subgroup property implications | View all subgroup property non-implications
Get more facts about intersection of kernels of bihomomorphisms|Get more facts about completely divisibility-closed subgroup


Suppose G is a group and H is an intersection of kernels of bihomomorphisms in G. Then, H is a completely divisibility-closed subgroup of G.

Facts used

  1. Kernel of a bihomomorphism implies completely divisibility-closed
  2. Complete divisibility-closedness is strongly intersection-closed


The proof follows directly from Facts (1) and (2).