Recently in a paper we get the following result:

Let a discrete group $\Gamma$ act on a discrete abelian group $G$ by group automorphisms. Every irreducible unitary representation $\pi$ of $G\rtimes\Gamma$ on a Hilbert space $H$ satisfies $\dim{H_\Gamma}\leq 1$. Here $H_\Gamma$ is the space of $\Gamma$-invariant vectors in $H$.

We are not experts in representation theory. My question is : Does this result appear in the literature before?

Recently in a paper we get the following result:

Let a discrete group $\Gamma$ act on a discrete abelian group $G$ by group automorphisms. Every irreducible unitary representation $\pi$ of $G\rtimes\Gamma$ on a Hilbert space $H$ satisfies $\dim{H_\Gamma}\leq 1$. Here $H_\Gamma$ is the space of $\Gamma$-invariant vectors in $H$.

We are not experts in representation theory.

My question is :

Does this result appear in the literature before?