Join of two finite subnormal subgroups is subnormal

History
This result was proved by Wielandt in ''Eine Verallgemeinerung der invarianten Untergruppen. Math. Z.45, 209–244 (1939).''

Statement
Suppose $$H$$ and $$K$$ are two fact about::finite subnormal subgroups of a group $$G$$. Then, the join of $$H$$ and $$K$$ is also a fact about::subnormal subgroup of $$G$$.