  A finite transitive permutation group is said to be 3/2-transitive if all the
nontrivial orbits of a point stabilizer have the same size greater than 1.
Examples include the 2-transitive groups, Frobenius groups and several other
less obvious ones. We prove that 3/2-transitive groups are either affine or
almost simple, and classify the latter. One of the main steps in the proof is
an arithmetic result on the subdegrees of groups of Lie type in characteristic
$p$: with some explicitly listed exceptions, every primitive action of such a
group is either 2-transitive, or has a subdegree divisible by $p$.

Group Theory