A New Upper Bound on Rubik's Cube Group
  In this paper we give a upper bound of 40 on Rubik's cube group. The previously known upper bound has been 42 since 1995. In order to prove our claim we use computational methods. The program used is GAP computer algebra. Further more we give the number of elements of given length in two important subgroups of Rubik's cube group. 
Silviu Radu