Join-transitively automorph-conjugate subgroup

Symbol-free definition
A subgroup of a group is termed join-transitively automorph-conjugate if its join with any automorph-conjugate subgroup is an automorph-conjugate subgroup.

Definition with symbols
A subgroup $$H$$ of a group $$G$$ is termed join-transitively automorph-conjugate if, for any automorph-conjugate subgroup $$K$$ of $$G$$, the subgroup $$\langle H, K \rangle$$ is also an automorph-conjugate subgroup.

Stronger properties

 * Weaker than::Characteristic subgroup:

Weaker properties

 * Stronger than::Automorph-conjugate subgroup
 * Stronger than::Join of automorph-conjugate subgroups
 * Stronger than::Closure-characteristic subgroup
 * Stronger than::Core-characteristic subgroup

Incomparable properties

 * Intermediately automorph-conjugate subgroup
 * Intersection-transitively automorph-conjugate subgroup