Published online by Cambridge University Press: 17 April 2009
Let G be a permutation group on a set Ω with no fixed points in Ω and let m be a positive integer. Then we define the movement of G as, m := move(G) := supΓ{|Γg \ Γ| │ g ∈ G}. Let p be a prime, p ≥ 5. If G is not a 2-group and p is the least odd prime dividing |G|, then we show that n := |Ω| ≤ 4m – p + 3.
Moreover, if we suppose that the permutation group induced by G on each orbit is not a 2-group then we improve the last bound of n and for an infinite family of groups the bound is attained.