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 (ₚ) ) ₓ₎ₑₒ up to isomorphism. The method illustrates techniques for eliminating possible structures that can appear as a subgroup of E (Q^ab) ₓ₎ₑₒ.