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![[parent]](http://images.planetmath.org:8080/images/uparrow.png) Viewing Correction to 'divisible group'
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theorems by yark
Correction id: 2235
Filed on: 2003-07-24 03:36:21
Status: Accepted on 2003-07-24 10:02:32
Type: Addendum
Correction text:
The term is sometimes used for non-abelian groups too, so you might consider enlarging the definition to allow that.
There are some interesting theorems about divisible abelian groups which could be mentioned:
1. If $D$ is a divisible abelian group, $A$ is an abelian group and $S$ is a subgroup of $A$, then any homomorphism from $S$ into $D$ can be extended to a homomorphism from $A$ into $D$.
2. Any divisible abelian group is isomorphic to the direct sum of its torsion subgroup and $n$ copies of the group of rationals (for some cardinal number $n$).
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No comment from object owner mathcam.
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