I say in advance that I am really new to Group Theory, so if my question is trivial I apologize in advance.

Let $A$ and $H$ be groups and $\Omega$ be a $H$-set. In this set-up, we can define the wreath product $ G: =A\,\text{Wr}_\Omega H$. If $A$ acts on set $\Lambda$, then we get a canonical action of $G$ on the set $\Lambda^\Omega=\lbrace f\colon \Omega \longrightarrow \Lambda| \: f \textit{ is a function}\rbrace$. Wikipedia calls this action **the primitive action of the wreath product**. My question is the following:

**Q:** Is the action above indeed primitive? If it is not, do we have to assume something more on the action of $A$ on $\Lambda$ ( for example primitivity) to ensure the primitivity of the action of the wreath product?

Any help or reference is well accepted. Thank you.