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ACCESSIBLE PROBLEMS IN FINITE GROUP THEORY OR HOW MUCH DO YOU REALLY KNOW ABOUT RUBIK'S CUBE? Tony Fisher, December 16, 2011 Abstract: A general introduction to groups is given, along with the basics of permutation groups and some key subgroups of Sn. The group of the 3x3x3 Rubik’s cube is introduced, with a look at some stabilizing subgroups. In particular, the group which “stabilizes the cube” (i.e., does not move any of the twenty-seven sub-cubes but does move the faces) is analyzed. A result by Yuri Lin (HCHS Class of 2007) is presented, along with a related unsolved problem. Explorations related to other Rubik’s Cube-like objects are suggested. Core Branches of Mathematics The Mathematics Subject Classification (MSC) scheme was developed by the American Mathematical Society and Zentralblatt für Mathematik. Broad subdivisions of Mathematics: Foundations (Logic, etc.) (Abstract) Algebra and Number Theory Geometry and Topology Mathematical Analysis including Applied and related areas: Computer and Information Sciences Probability and Statistics Physical Sciences and Engineering History, Education, Other From, e.g., http://ratnu.tripod.com/mathbranches.html