Verbally complete group

Definition
A group $$G$$ is termed a verbally complete group if every word map corresponds to a word that does not reduce (in the free group sense) to the identity element is surjective. In other words, for any word $$w(x_1,x_2,\dots,x_n)$$ and any element $$g \in G$$, there exist solutions in $$G$$ to $$w(x_1,x_2,\dots,x_n) = g$$.