Amalgam-strictly characteristic subgroup

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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 $G*_{H}G$.

Formalisms

In terms of the in-amalgam operator

This property is obtained by applying the in-amalgam operator to the property: strictly characteristic subgroup
View other properties obtained by applying the in-amalgam operator

Relation with other properties

Stronger properties

• Amalgam-normal-subhomomorph-containing subgroup
  • Finite normal subgroup
  • Periodic normal subgroup
• Central subgroup: For full proof, refer: Central implies amalgam-strictly characteristic
• Normal subgroup contained in the hypercenter: For full proof, refer: Normal subgroup contained in the hypercenter is amalgam-strictly characteristic

Weaker properties

• Amalgam-characteristic subgroup
• Potentially strictly characteristic subgroup
• Potentially characteristic subgroup
• Normal subgroup