I will talk about a problem of Ellis and Pestov's conjecture about its full resolution. The problem of Ellis comes purely from topological dynamics and has been answered in the negative for the dicrete group of integers by Glasner and independently by Pestov for the group of order preserving automorphisms of the rationals with the use of Ramsey theory. We extend the negative answer to the group of permutations of integers and prove a stronger result that also relies on Ramsey theory.