Join of automorph-conjugate subgroups

Definition
A subgroup of a group is termed a join of automorph-conjugate subgroups or AC-generated if it is generated by a collection of automorph-conjugate subgroups, viz it is a join of automorph-conjugate subgroups.

Stronger properties

 * Automorph-conjugate subgroup
 * Hall subgroup

Weaker properties

 * Closure-characteristic subgroup

Conjunction with other properties
Any normal subgroup that is a join of automorph-conjugate subgroups is characteristic.