五魔方的群结构
首发时间:2018-07-27
摘要:从群论的角度去研究魔方的变换是近年来新兴的一个课题.David Joyner 给出了普通三阶魔方变换的群结构.本文推广他的工作,给出了五魔方的变换群的一个表示方式,并证明了五魔方群$\widetilde{G}\cong(C_{3}^{19} \rtimes A_{20}) \times (C_{2}^{29} \rtimes A_{30})$.
关键词: 交错群;循环群;五魔方;五魔方群;半直积
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The Group Structure of the Megaminx
Abstract:Studying the Rubik's Cube by using group theory is one of the interesting topics in recent years. David Joyner has found out the group structure of the Rubik's Cube. In our paper,we generalize his result to the case of Megaminx, we have found out a way to represent this group and prove that the Megaminx group $\widetilde{G}\cong(C_{3}^{19} \rtimes A_{20}) \times (C_{2}^{29} \rtimes A_{30})$.
Keywords: alternating group cyclic group Megaminx Megaminx group semidirect product
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