Editing Direct sum of groups (section)

{{Use American English|date = January 2019}}
{{Short description|Means of constructing a group from two subgroups}}
{{Cleanup rewrite|several issues are raised on the discussion page|date=March 2013}}
{{Group theory sidebar |Basics}}

In [[mathematics]], a [[group (mathematics)|group]] ''G'' is called the '''direct sum'''<ref name=":0">Homology. Saunders MacLane. Springer, Berlin; Academic Press, New York, 1963.</ref><ref name=":1">László Fuchs. Infinite Abelian Groups</ref> of two [[Normal subgroup|normal subgroups]] with [[Trivial group|trivial intersection]] if it is [[Generating set of a group|generated]] by the subgroups. In [[abstract algebra]], this method of construction of groups can be generalized to direct sums of [[vector space]]s, [[module (mathematics)|modules]], and other structures; see the article [[direct sum of modules]] for more information. A group which can be expressed as a direct sum of non-trivial subgroups is called ''decomposable'', and if a group cannot be expressed as such a direct sum then it is called ''indecomposable''.