Amalgam-normal-subhomomorph-containing subgroup

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This article defines a subgroup property: a property that can be evaluated to true/false given a group and a subgroup thereof, invariant under subgroup equivalence. View a complete list of subgroup properties[SHOW MORE]

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Definition

A subgroup $H$ of a group <amth>G</math> is termed an amalgam-normal-subhomomorph-containing subgroup if the amalgamated subgroup $H$ is a normal-subhomomorph-containing subgroup in the amalgamated free product $G{*}_{H}G$.

Formalisms

In terms of the in-amalgam operator

This property is obtained by applying the in-amalgam operator to the property: normal-subhomomorph-containing subgroup
View other properties obtained by applying the in-amalgam operator

Relation with other properties

Stronger properties

• Finite normal subgroup
• Periodic normal subgroup

Weaker properties

• Amalgam-strictly characteristic subgroup
• Amalgam-characteristic subgroup
• Potentially normal-subhomomorph-containing subgroup
• Potentially strictly characteristic subgroup
• Potentially characteristic subgroup
• Normal subgroup