Homomorphism-closed subgroup

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

Definition with symbols

A subgroup $H$ of a group $G$ is termed a homomorphism-closed subgroup (or sometimes, simply a closed subgroup) if every homomorphism from $H$ to $G$ extends uniquely to an endomorphism of $G$.

Relation with other properties

Weaker properties

• Nearly closed subgroup

References

• On a question of Farjoun by Michael Aschbacher, Finite Groups 2003 published by Walter de Gruyter