The Classification of Permutation Groups with Maximum Orbits (JOURNAL OF ADVANCES IN MATHEMATICS, 2018)
Let G be a permutation group on a set with no fixed points in and let m be a positive integer. If no element of G moves any subset of by more than m points (that is, if for every and g 2 G), and the lengths two of orbits is p, and the restof orbits have lengths equal to 3. Then the number t of G-orbits in is at most  Moreover, we classifiy all groups for is hold.(For  denotes the greatest integer less than or equal to x.)