Periodic normal implies image-potentially characteristic

Statement
Suppose $$H$$ is a periodic normal subgroup of a group $$G$$. Then, $$H$$ is an image-potentially characteristic subgroup of $$G$$.

Related facts

 * Finite normal implies image-potentially characteristic, because finite normal implies amalgam-characteristic
 * Central implies image-potentially characteristic, because central implies amalgam-characteristic
 * Normal subgroup contained in hypercenter is image-potentially characteristic, because normal subgroup contained in hypercenter is amalgam-characteristic
 * Periodic normal implies potentially characteristic

Facts used

 * 1) uses::Periodic normal implies amalgam-characteristic
 * 2) uses::Amalgam-characteristic implies image-potentially characteristic

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