Join of all abelian normal subgroups

Definition
Suppose $$G$$ is a group. The join of all abelian normal subgroups of $$G$$ is the subgroup of $$G$$ defined as the join of all the abelian normal subgroups of $$G$$.

If $$G$$ is a finite group (or more generally a group satisfying ascending chain condition on normal subgroups) then this is equivalent to the join of all subgroups that are maximal among abelian normal subgroups.

Facts

 * Join of all abelian normal subgroups is isoclinism-invariant