Research Of Rubik’s Cube Group

This paper introduced group theory to Rubik’s cube, from the perspective of group theory to study the rubik’s cube rotation. First three chapters given some results of Rubik’s cube group. Introduces the basic concepts of Rubik’s cube, and obtained the sufficient and necessary conditions of the elements in Rubik’s cube group, then found the structure of cube group G through a simple method, and further studied on Rubik’s cube by the structure. Researched two special subgroups of G the next, and proved the two-adjacent-faces group and projective group PGL(2,5) are isomorphic, and PSL(2,7) is a subgroup of the cross group, thus know it actually acts2-transitively on corner cube.Finally, researched Rubik’s cube of order n, given the concept of generalized cube group, as the focus of this article given the structure of its rotation group in chapter4.