A Necessary Condition for Transitivity of a Finite Permutation Group
Marston Conder, John McKay · Bulletin of the London Mathematical Society · 1988
Suppose the group G is generated by permutations g1, g2, …, g8 acting on a set Ω of size n, such that g1g2…g8 is the identity permutation. If the generator gi has exactly ci cycles (for 1 ⩽ i ⩽ s), and G is transitive on Ω, then n(s−2)−∑i=18ci+2 is a non-negative even integer. This is proved using an elementary graph-theoretic argument.