MATH W4041:
Intro to Modern Algebra I
Spring 2010
Please read "Chapter 2. Groups" from our textbook, Artin. This will take several weeks.
Please study the handout "Triangle Orbits". For each triangle, what symmetries of the triangle stabilize (don't change) that pattern? Which symmetries take that pattern to a specific other pattern in the same orbit (connected cluster)? For the other patterns in the same orbit, does the same set of symmetries stabilize those patterns? If not, how are the stabilizers related?
This is an open-ended "stare at the picture" problem, that will make more sense as the semester goes on.