Verbal subgroup of finite type

Definition
Suppose $$G$$ is a group and $$H$$ is a subgroup of $$G$$. We say that $$H$$ is a verbal subgroup of finite type in $$G$$ if the following equivalent conditions hold:


 * 1) There exists a single word $$w$$ in $$n$$ letters for some positive integer $$n$$ such that $$H$$ is the image of the word map corresponding to $$w$$.
 * 2) There exists a finite collection $$C$$ of words $$w$$ (each with $$n_w$$ letters) such that $$H$$ is the union of the images of the word maps $$G^{n_w} \to G$$.