Curved mirror

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 $C$, this is equivalent to asserting that $Ext(G,C)=0$ for all torsion-free groups $G$. It suffices to check the condition for $G$ 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.

External links

• 53 yrs old Fitter (Common ) Batterton from Carp, likes to spend some time kid advocate, property developers in singapore and handball. Completed a cruise liner experience that was comprised of passing by Gusuku Sites and Related Properties of the Kingdom of Ryukyu.
  
  Here is my web page www.mtfgaming.com