Indivisibility of the class number of a real abelian field of prime conductor

For a fixed integer $n \geq 1$, let $p=2n\ell +1$ be a prime number with an odd prime number $\ell $ and let $F=F_{p,\ell }$ be the real abelian field of conductor $p$ and degree $\ell $. We prove that for each fixed $n$, there exist only finitely many pa