1-endomorphism-invariant 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 1-endomorphism-invariant if, given any 1-endomorphism $\phi$ of $G$, $\phi (H)\subseteq H$.

Relation with other properties

Weaker properties

• Quasiendomorphism-invariant subgroup
• Fully characteristic subgroup
• 1-automorphism-invariant subgroup
• Characteristic subgroup