Normal subgroup of Wielandt subgroup

Definition
A subgroup of a group is termed a normal subgroup of Wielandt subgroup if it satisfies the following equivalent conditions:


 * 1) It is a defining ingredient::normal subgroup of the defining ingredient::Wielandt subgroup.
 * 2) It is a defining ingredient::subnormal subgroup of the Wielandt subgroup.
 * 3) It is a defining ingredient::subnormal subgroup of the whole group and normalizes every defining ingredient::subnormal subgroup.

Weaker properties

 * Stronger than::Normal subgroup of characteristic subgroup
 * Stronger than::2-subnormal subgroup
 * Stronger than::Subgroup contained in the Wielandt subgroup
 * Stronger than::Subnormal-permutable subnormal subgroup