Statistique sur la cyclicité de A-module de Drinfeld de rang 2

Let $\Phi $ be a Drinfeld $\mathbf{F}{q}[T]$-module of rank $2$, over a finite field $L=\mathbf{F}{q^{n}}$. We will study the cyclic property of the structure $L^{\Phi }.$ We will prove that the latter is cyclic only for trivial extensions of $\mathbf{F}_{q}$.