  We consider the gauging of $ SL(2,R) $ WZNW model by its nilpotent subgroup
E(1). The resulting space-time of the corresponding sigma model is seen to
collapse to a one dimensional field theory of Liouville. Gauging the diagonal
subgroup $ E(1) \times U(1) $ of $SL(2,R) \times U(1)$ theory yields an
extremal three dimensional black string. We show that these solutions are
obtained from the two dimensional black hole of Witten and the three
dimensional black string of Horne and Horowitz by boosting the gauge group.
