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 Finite subnormal subgroup (?)s of a group $G$. Then, the join of $H$ and $K$ is also a Subnormal subgroup (?) of $G$.