Torsion groups of elliptic curves over the $\mathbb Z_p$-extensions of $\mathbb Q$

Abstract: We determine, for an elliptic curve $E/\mathbb Q$ and for all $p$, all the possible torsion groups $E(\mathbb Q_{\infty, p}){tors}$, where $\mathbb Q{\infty, p}$ is the $\mathbb Z_p$-extension of $\mathbb Q$.