We prove the following result, solving a problem raised in an article by A.
Buium and Ph. J. Cassidy, to appear in the collected works of E. Kolchin.
If G is a differential algebraic group whose underlying set is some affine
n-space, then G is unipotenr. A key result, possibly of independent interes
t, concerns infinite-dimensional group schemes: a group scheme whose underl
ying scheme is Spec(K[X-1, X-2, ...]) (K an algebraically closed field of c
haracteristic 0) is a projective limit of unipotent algebraic groups.