Homomorphism-closed 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]


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


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