Date of Graduation
Spring 2012
Degree
Master of Science in Mathematics
Department
Mathematics
Committee Chair
Kishor Shah
Abstract
We study some of the group theory underlying the 3x3x3 Rubik's Cube. We prove the well-known Fundamental Theorem of Cubology for the 3x3x3 Rubik's Cube, filling in various details. We introduce and study four interesting subgroups of the 3x3x3 Rubik's Cube Group. In addition, we study the well-known Slice Group, again filling in various details. The group theory of the 5x5x5 Rubik's Cube is not well-developed in mathematical literature. We introduce and study some group theory for the 5x5x5 Rubik's Cube, which, to our knowledge, may be new: we state and prove a Fundamental Theorem of Cubology for the 5x5x5 Rubik's Cube. We also introduce and study two groups which arise from the 5x5x5 Rubik's Cube: the Full Group and the Visual Group. We then examine the relationship between these two groups. We relate the 5x5x5 Rubik's Cube Group to the 3x3x3 Rubik's Cube Group. We conclude our thesis by making some brief comments on the (2n+1)x(2n+1)x(2n+1) Rubik's Cube.
Keywords
Group Theory, 3x3x3 Rubik's Cube, 5x5x5 Rubik's Cube, Slice Group, Semidirect Products
Subject Categories
Mathematics
Copyright
© Kristen Michelle Howell
Recommended Citation
Howell, Kristen Michelle, "Group Theory Underlying the 3x3x3 and 5x5x5 Rubik's Cubes" (2012). MSU Graduate Theses. 1640.
https://bearworks.missouristate.edu/theses/1640
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