

GAP Projects In studying abstract algebra, the process of experimentation, conjecture, and proof is strongly inhibited by a lack of data. While it is true that a good textbook will contain many wellknown examples, those examples are usually introduced in the context of a single specific topic. Exploring an example in more depth or in a different context typically requires a prohibitive amount of computation.
GAP Primer  A supplemental resource and reading assignment for the class. Project 1.  An Introduction to GAP Illustrates the basics of GAP in the context of the group of rotations of a cube; Assumes no prior knowledge of GAP
Project 2.  Subgroups Generated by Subsets Discusses subgroups generated by a subset from two viewpoints: the "topdown" approach using intersections, and the "bottomup" approach using group closure
Project 3.  Exploring Rubik's Cube with GAP Investigates the transformation group of Rubik's cube.
Project 4.  Conjugation in Permutation Groups Explores the relationship between the cycle structure of a permutation and cycle structure of its conjugate; Revisits permutations of the Rubik's cube.
Project 5.  Exploring Normal Subgroups and Quotient Groups.
Project 6.  The Number of Groups of a Given Order Explores the number of possible group structures for any given order; the class will need hints and encouragement on the last problem!
Questions or Comments? Email: holdenerj@kenyon.edu or blanchpf@muohio.edu 

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