Generalization of Rubik's cube group to n-dimensional case

In this paper, Rubik's cube group in n-dimensional case is described. In that case, some interesting effects arise, which is related with angular rotations. For n = 4, the group Z(3) arises, which can be realized as a factor group of A(4) by commutation [A(4), A(4)] = V-4. For n >= 5 there are no such effects, because corresponding factor is trivial. Rubik's cube is an important model to study effects of groups related with, in particular, holonomy groups from differential geometry.