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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 vectorshave the same size. We complete the classification of all the (1/2)-transitivelinear groups. As a consequence we complete the determination of the finite(3/2)-transitive permutation groups -- the transitive groups for which apoint-stabilizer has all its nontrivial orbits of the same size. We alsodetermine the finite (k+1/2)-transitive permutation groups for integers k > 1.

The classification of (3/2)-transitive permutation groups and (1/2)-transitive linear groups