Iterated agemo implies verbal

This article gives the statement and possibly, proof, of an implication relation between two subgroup properties. That is, it states that every subgroup satisfying the first subgroup property (i.e., iterated agemo subgroup of group of prime power order) must also satisfy the second subgroup property (i.e., verbal subgroup of group of prime power order)
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Statement

Suppose $G$ is a group of prime power order and $H$ is an iterated agemo subgroup of $G$. Then, $H$ is also a verbal subgroup of $G$.

Facts used

1. Agemo subgroups are verbal
2. Verbality is transitive

Proof

The proof follows from facts (1) and (2).