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.
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