Editing Direct sum of groups (section)

==Examples==

* If we take  <math display="inline"> G= \prod_{i\in I} H_i </math> it is clear that <math> G </math> is the direct product of the subgroups <math display="inline"> H_{i_0} \times \prod_{i\not=i_0}H_i</math>.

* If <math>H</math> is a [[Divisible group|divisible subgroup]] of an abelian group <math>G</math> then there exists another subgroup <math>K</math> of <math>G</math> such that <math>G=K+H</math>.
* If <math>G</math> also has a [[vector space]] structure then <math>G</math> can be written as a direct sum of <math>\mathbb R</math> and another subspace <math>K</math> that will be isomorphic to the quotient <math>G/K</math>.