Automorph-join-closed subnormal subgroup

Definition
A subgroup of a group is termed automorph-join-closed subnormal if the join of any collection of subgroups that are automorphic to it (i.e., its images under automorphisms of the whole group) is a subnormal subgroup.

Stronger properties

 * Weaker than::Normal subgroup
 * Weaker than::2-subnormal subgroup
 * Weaker than::Subnormal subgroup of finite index

Weaker properties

 * Stronger than::Conjugate-join-closed subnormal subgroup
 * Stronger than::Finite-automorph-join-closed subnormal subgroup
 * Stronger than::Finite-conjugate-join-closed subnormal subgroup

Facts

 * Any automorph-join-closed subnormal subgroup of a normal subgroup is conjugate-join-closed subnormal.