Group admitting a partition into abelian subgroups

Definition
A group admitting a partition into abelian subgroups is defined as a group that can be expressed as a union of defining ingredient::abelian subgroups (i.e., subgroups that are all defining ingredient::abelian groups) of which any two have trivial intersection. In other words, it admits a fact about::partition of a group where all the parts are abelian subgroups.

Note that any nontrivial group with this property is a group admitting a nontrivial partition.