Periodic normal implies potentially characteristic

Statement
A periodic normal subgroup of a group is a potentially characteristic subgroup.

Similar facts

 * Finite normal implies potentially characteristic, uses finite normal implies amalgam-characteristic.
 * Central implies potentially characteristic, uses central implies amalgam-characteristic.
 * Normal subgroup contained in hypercenter is potentially characteristic, uses normal subgroup contained in hypercenter is amalgam-characteristic.
 * Abelian implies every subgroup is potentially characteristic
 * Nilpotent implies every normal subgroup is potentially characteristic
 * Group with no element of order p implies every p-divisible normal subgroup is potentially characteristic

Facts used

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

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