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- Cotorsion_group abstract "In mathematics, in the realm of abelian group theory, an abelian group is said to be cotorsion if every extension of it by a torsion-free group splits. If the group is , this is equivalent to asserting that for all torsion-free groups . It suffices to check the condition for being the group of rational numbers.Some properties of cotorsion groups: Any quotient of a cotorsion group is cotorsion. A direct product of groups is cotorsion if and only if each factor is. Every divisible group or injective group is cotorsion. The Baer Fomin Theorem states that a torsion group is cotorsion if and only if it is a direct sum of a divisible group and a bounded group, that is, a group of bounded exponent. A torsion-free abelian group is cotorsion if and only if it is algebraically compact. Ulm subgroups of cotorsion groups are cotorsion and Ulm factors of cotorsion groups are algebraically compact.".
- Cotorsion_group wikiPageID "5739241".
- Cotorsion_group wikiPageRevisionID "479213206".
- Cotorsion_group first "L.".
- Cotorsion_group hasPhotoCollection Cotorsion_group.
- Cotorsion_group id "Cotorsion_group".
- Cotorsion_group last "Fuchs".
- Cotorsion_group oldid "18282".
- Cotorsion_group title "Cotorsion group".
- Cotorsion_group subject Category:Abelian_group_theory.
- Cotorsion_group subject Category:Properties_of_groups.
- Cotorsion_group type Abstraction100002137.
- Cotorsion_group type Possession100032613.
- Cotorsion_group type PropertiesOfGroups.
- Cotorsion_group type Property113244109.
- Cotorsion_group type Relation100031921.
- Cotorsion_group comment "In mathematics, in the realm of abelian group theory, an abelian group is said to be cotorsion if every extension of it by a torsion-free group splits. If the group is , this is equivalent to asserting that for all torsion-free groups . It suffices to check the condition for being the group of rational numbers.Some properties of cotorsion groups: Any quotient of a cotorsion group is cotorsion. A direct product of groups is cotorsion if and only if each factor is.".
- Cotorsion_group label "Cotorsion group".
- Cotorsion_group sameAs m.0f23g7.
- Cotorsion_group sameAs Q5175462.
- Cotorsion_group sameAs Q5175462.
- Cotorsion_group sameAs Cotorsion_group.
- Cotorsion_group wasDerivedFrom Cotorsion_group?oldid=479213206.
- Cotorsion_group isPrimaryTopicOf Cotorsion_group.