1-homomorphism of groups

From Groupprops
Jump to: navigation, search


Let G and H be groups. A map f:G \to H is termed a 1-homomorphism if it satisfies the following equivalent conditions:

  • For any element g \in G, the restriction of f to the cyclic subgroup generated by g, is a homomorphism of groups.
  • For any homomorphism from a cyclic group to G, the composite with f is also a homomorphism.

Relation with other properties

Stronger properties