Assertion: abelian group's subgroup | /r/HasProperty | invariant
Facets:
value: under surjective endomorphisms
type: OTHER
value: under all automorphisms
type: OTHER
value: under any automorphism of the group
type: OTHER
Source sentences:
text: Any subgroup obtained via a subgroup-defining function is invariant under any automorphism of the group, and is hence a characteristic subgroup.
text: Since Inn(G) ⊆ Aut(G) and a characteristic subgroup is invariant under all automorphisms, every characteristic subgroup is normal.
text: A strictly characteristic subgroup, or a distinguished subgroup, which is invariant under surjective endomorphisms.