Algebraically compact group
In
direct summand of every abelian group containing it as a pure subgroup
.
Equivalent characterizations of algebraic compactness:
- The reduced part of the group is Hausdorff and complete in the adic topology.
- The group is pure injective, that is, injective with respect to exact sequences where the embedding is as a pure subgroup.
Relations with other properties:
- A torsion-free group is cotorsionif and only if it is algebraically compact.
- Every injective groupis algebraically compact.
- Ulm factorsof cotorsion groups are algebraically compact.
External links
 | This group theory-related article is a stub. You can help Wikipedia by expanding it. |