  Let E be an elliptic curve defined over Q and let G = E(Q)_tors be the
associated torsion subgroup. We study, for a given G, which possible groups G
<= H could appear such that H=E(K)_tors, for [K:Q]=4 and H is one of the
possible torsion structures that occur infinitely often as torsion structures
of elliptic curves defined over quartic number fields.
