Download ACCESSIBLE PROBLEMS IN FINITE GROUP THEORY

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:
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Foundations (Logic, etc.)
(Abstract) Algebra and Number Theory
Geometry and Topology
Mathematical Analysis including
Applied and related areas:
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Computer and Information Sciences
Probability and Statistics
Physical Sciences and Engineering
History, Education, Other
From, e.g., http://ratnu.tripod.com/mathbranches.html