Amalgam-strictly characteristic subgroup

Definition
A subgroup $$H$$ of a group $$G$$ is termed amalgam-strictly characteristic if the amalgamated subgroup $$H$$ is a strictly characteristic subgroup in the amalgamated free product $$G *_H G$$.

Stronger properties

 * Weaker than::Amalgam-normal-subhomomorph-containing subgroup
 * Weaker than::Finite normal subgroup
 * Weaker than::Periodic normal subgroup
 * Weaker than::Central subgroup:
 * Weaker than::Normal subgroup contained in the hypercenter:

Weaker properties

 * Stronger than::Amalgam-characteristic subgroup
 * Stronger than::Potentially strictly characteristic subgroup
 * Stronger than::Potentially characteristic subgroup
 * Stronger than::Normal subgroup