Applications Of Group Theory In Rubik's Cube

This paper discussed the mathematical properties of the Rubik's cube from the viewpoint of group theory. First of all, taking the Rubik's cube as a tool, this paper demonstrated the practical applications of all kinds of concepts and their relevant properties in group theory, such as permutation, action, orbit, transitivity, primitivity, conjugation, commutator and homomorphism; secondly, this paper introduced the structure of the Rubik's cube group; At last, as the core of this paper, it promoted the lower bound of the diameter of the Cayley graph with respect to the Rubik's cube group, from 20 to 21.