Partition of a group

Definition
A partition of a group is an expression of the group as a set-theoretic union of subgroups, with pairwise trivial intersections.

The partition is said to be nontrivial if it uses more than one subgroup, or equivalently, if all the subgroups are proper.

Note that any nontrivial partition must involve at least three subgroups.

Not every group admits a nontrivial partition.