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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]


A subgroup H of a group G is termed a HEP-subgroup or is said to have the Homomorphism Extension Property if, for any homomorphism of groups \varphi:H \to G, there exists an endomorphism \varphi' of G such that the restriction of \varphi' to H equals \varphi.

Relation with other properties

Stronger properties

Weaker properties