Consequence of Schreier-Sims Algorithm in Solving Rubiks Cube

Successful computation with a permutation group is largely depended on our ability to find an effective representative for the group. In particular many calculations can be facilitated if we have a coset representative for each subgroup of the chain in its predecessor. So we have tried in this book to construct a chain in which each subgroup is a point stabilizer of the last. These concepts were introduced by Schrier-Sims as an effective description of a permutation group. For the holistic idea we have described various versions of the Schreier-Sims Algorithm. Finally in solving Rubiks Cube, we have thoroughly discussed the structure and various subgroups of Rubiks Cube before applying the Schreier-Sims Algorithm. These subgroups are easier to understand and solve. We have marked the 48 moving squares to convert the twists of Rubiks Cube in to permutation cycle. Handling an enormous group like the Rubiks Cube Group becomes very easy when we use the Schreier-Sims Algorithm to form the stabilizer chain of the Rubiks Cube Group. This stabilizer chain was then used to factorize a random element of the Rubiks Cube Group, which will lead us to the solution of the Rubiks Cube.