Group satisfying subnormal join property

Definition
A group is said to satisfy the subnormal join property if it satisfies the following equivalent conditions:


 * 1) The join (i.e., subgroup generated) of two fact about::subnormal subgroups of the group is again subnormal.
 * 2) The join of a finite collection of subnormal subgroups of the group is again subnormal.
 * 3) The commutator of any two subnormal subgroups of the group is again subnormal.

Textbook references

 * , Page 388 (definition in paragraph)