The Size of a Minimal Generating Set for Primitive3/2 -Transitive Groups

We refer to d(G) as the minimal size of a generating set ofa finite group G, and say that G is d -generated if d(G)≤ d.A transitive permutation group G is called 3/2-transitive ifthe point stabilizer G_αis nontrivial and its orbits distinct from α are of the same size.We prove that d(G)≤ 4 for every primitive 3/2-transitive permutation group G and, moreover,G is 2-generated except for the rather particular solvable affine groupsthat we describe completely.In particular, all finite 2-transitive and 2-homogeneous groups are 2-generated.We also show that every finite group whose abelian subgroups are cyclic is 2-generated,and so is every Frobenius complement.