Hochschild cohomology of a smash product in the nonsemisimple case

In this paper we explore the relations between the Hochschild cohomology of an algebra over some field and the Hochschild cohomology of its smash product with a finite group. Basically we are concentrated on the case where the group under consideration is an extension of a cyclic $p$-group by some $p^{\mathrm{\prime }}$-group, where $p$ is the characteristic of the ground field.