A group $G$ is said to enjoy ``Hasse principle'' if every local coboundary of $G$ is a global coboundary. It is proved that every group of order $p^4$ and every metacyclic group enjoy ``Hasse principle''.
Manoj Kumar. Lekh Raj Vermani. "``Hasse principle'' for groups of order $p^4$." Proc. Japan Acad. Ser. A Math. Sci. 77 (6) 95 - 98, June 2001. https://doi.org/10.3792/pjaa.77.95