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Let E be an elliptic curve over the rationals. Let L be an infinite Galoisextension of the rationals with uniformly bounded local degrees at almost allprimes. We will consider the infinite extension L(E_tor) of the rationals wherewe adjoin all coordinates of torsion points of E. In this paper we will provean effective lower bound for the height of non-zero elements in L(E_tor) thatare not a root of unity.

Small Heights in Large Non-Abelian Extensions