  A linear group G on a finite vector space V, (that is, a subgroup of GL(V))
is called (1/2)-transitive if all the G-orbits on the set of nonzero vectors
have the same size. We complete the classification of all the (1/2)-transitive
linear groups. As a consequence we complete the determination of the finite
(3/2)-transitive permutation groups -- the transitive groups for which a
point-stabilizer has all its nontrivial orbits of the same size. We also
determine the finite (k+1/2)-transitive permutation groups for integers k > 1.
