Amalgam-normal-subhomomorph-containing subgroup

Definition
A subgroup $$H$$ of a group $$G$$ is termed an amalgam-normal-subhomomorph-containing subgroup if the amalgamated subgroup $$H$$ is a normal-subhomomorph-containing subgroup in the amalgamated free product $$G *_H G$$.

Stronger properties

 * Weaker than::Finite normal subgroup
 * Weaker than::Periodic normal subgroup

Weaker properties

 * Stronger than::Amalgam-strictly characteristic subgroup
 * Stronger than::Amalgam-characteristic subgroup
 * Stronger than::Potentially normal-subhomomorph-containing subgroup
 * Stronger than::Potentially strictly characteristic subgroup
 * Stronger than::Potentially characteristic subgroup
 * Stronger than::Normal subgroup