Group-closed automorphism property

From Groupprops
Jump to: navigation, search

Template:Automorphism metaproperty


An automorphism property is termed group-closed if the set of automorphisms of a group which satisfy the given property form a subgroup of its automorphism group. In fact, if they do form a subgroup, that subgroup must be a normal subgroup (it need not, however, always be a characteristic subgroup of the automorphism group).