Abstract
This paper expounds the basic concept of group theory and its application in Rubiks Cube transformation and restoration formula. The different states of the magic cube are regarded as the elements of the magic cube group, and the set generated by six basic operations is equivalent to the homomorphism of the magic cube group for analysis, from the mathematical characteristics of the permutation group to some practical examples. The collection of possible states of Rubik's Cube is a group, called Rubik's Cube Group, which can be analyzed with the knowledge of group theory. The essence of the magic cube group is the subgroup of the substitution group. There are six basic operations of the magic cube. The combination of basic operations can only produce even pairs of blocks to exchange positions or flip directions at the same time. Therefore, there are some restrictions on the transformation of the magic cube. Some practical examples give some ideas for creating the magic cube formula.
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