The subgroup "G" × {0} of "G" ⊕ "H" is isomorphic to "G" and is often identified with "G"; similarly for {0} × "H" and "H". (See "internal direct sum" below.) With this identification, it is true that every element of "G" ⊕ "H" can be written in one and only one way as the sum of an element of "G" and an element of "H". The rank of "G" ⊕ "H" is equal to the sum of the ranks of "G" and "H".