  Let $E$ be an elliptic curve defined over $\mathbb{Q}$. Let $p>3$ be a prime
such that $p-1$ is not divisible by $3,4,5,7,11$. In this article we classify
the groups that can arise as $E(\mathbb{Q}(\zeta_p))_{\text{tors}}$ up to
isomorphism. The method illustrates techniques for eliminating possible
structures that can appear as a subgroup of $E(\mathbb{Q}^{ab})_{\text{tors}}.$
