Hy , I would like to have some help on the following problem , if it is possible . Any contribution is welcom .
let $E$ a $K$ vectoriel space of dimension $n\geq 1$ , and $K$ finite field of cardinal $q$ . Suppose that $L(E)$ is being provided by the uniform probability law . let $p_{n}(q)$ the probability of an endomorphism being a cyclic endomorphism , compute $ \lim_{q \to \infty} p_{n}(q)$ .
I am guessing the probability must be $1$ , I am looking for a minoration .