  Let k be an algebraically closed field of characteristic 2, and let W be the
ring of infinite Witt vectors over k. Let S_4 denote the symmetric group on 4
letters. We determine the universal deformation ring R(S_4,V) for every
kS_4-module V which has stable endomorphism ring k and show that R(S_4,V) is
isomorphic to either k, or W[t]/(t^2,2t), or the group ring W[Z/2]. This gives
a positive answer in this case to a question raised by the first author and
Chinburg whether the universal deformation ring of a representation of a finite
group with stable endomorphism ring k is always isomorphic to a subquotient
ring of the group ring over W of a defect group of the modular block associated
to the representation.
