Torsion of Rational Elliptic Curves over the Cyclotomic Extensions of Q

Let E be an elliptic curve defined over 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(Q(ζₚ))ₜₒᵣₛ up to isomorphism. The method illustrates techniques for eliminating possible structures that can appear as a subgroup of E(Qᵃᵇ)ₜₒᵣₛ.