Potentially 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 $G$ is termed a potentially normal-subhomomorph-containing subgroup if there exists a group $K$ containing $G$ such that $H$ is a normal-subhomomorph-containing subgroup of $K$.

Formalisms

In terms of the potentially operator

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

Relation with other properties

Stronger properties

• Normal-subhomomorph-containing subgroup
• Amalgam-normal-subhomomorph-containing subgroup
  • Finite normal subgroup
  • Periodic normal subgroup

Weaker properties

• Potentially strictly characteristic subgroup
• Potentially characteristic subgroup
• Normal subgroup