Completely divisibility-closed normal subgroup
This page describes a subgroup property obtained as a conjunction (AND) of two (or more) more fundamental subgroup properties: completely divisibility-closed subgroup and normal subgroup
View other subgroup property conjunctions | view all subgroup properties
- is both a normal subgroup of and a completely divisibility-closed subgroup of .
- is a normal subgroup of , and for any prime number such that is -divisible, the quotient group is -torsion-free.
Relation with other properties
|Property||Meaning||Proof of implication||Proof of strictness (reverse implication failure)||Intermediate notions|
|kernel of a bihomomorphism||kernel of a bihomomorphism implies completely divisibility-closed|
|intersection of kernels of bihomomorphisms||intersection of kernels of bihomomorphisms implies completely divisibility-closed|