A group $G$ is said to enjoy ``Hasse principle'' if every local coboundary of $G$ is a global coboundary. It is proved that every non-Abelian finite $p$-group having a miximal subgroup which is cyclic and every extraspecial $p$-group enjoy ``Hasse principle''.
Manoj Kumar. Lekh Raj Vermani. "``Hasse principle'' for extraspecial $p$-groups." Proc. Japan Acad. Ser. A Math. Sci. 76 (8) 123 - 125, Oct. 2000. https://doi.org/10.3792/pjaa.76.123