Assertion: abelian group's subgroup | /r/HasProperty | obtained via subgroup-defining function
Facets:
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 any subgroup-defining function (such as the center, the derived subgroup, the Frattini subgroup, the Fitting subgroup etc.) returns a characteristic subgroup of the whole group, and since every characteristic subgroup is normal, any subgroup obtained via a subgroup-defining function must be either trivial or the whole group.