Semiregular elements in cubic vertex-transitive graphs and the   restricted Burnside problem
  In this paper, we prove that the maximal order of a semiregular element in the automorphism group of a cubic vertex-transitive graph X does not tend to infinity as the number of vertices of X tends to infinity. This gives a solution (in the negative) to a conjecture of Peter Cameron, John Sheehan and the author.   However, with an application of the positive solution of the restricted Burnside problem, we show that this conjecture holds true when X is either a Cayley graph or an arc-transitive graph. 
Pablo Spiga
math.CO