Verbality satisfies image condition
This article gives the statement, and possibly proof, of a subgroup property (i.e., verbal subgroup) satisfying a subgroup metaproperty (i.e., image condition)
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Suppose is a group, is a verbal subgroup of , and is a homomorphism of groups. Then, the image is a verbal subgroup of . In fact, if is the span of a collection of words in terms of the elements of , then is the span of the same collection of words in terms of the elements of .