4023f10ex3

4023f10ex3 - Name: Exam 3 Instructions. Answer each of the...

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Unformatted text preview: Name: Exam 3 Instructions. Answer each of the questions on your own paper, and be sure to show your work so that partial credit can be adequately assessed. Credit will not be given for answers (even correct ones) without supporting work. Put your name on each page of your paper. 1. [30 Points] (a) Fill in the missing parts to complete the statement of Burnsides Theorem: If u1D43A is a finite group that acts on a finite set u1D44B , then the number u1D441 of distinct orbits is: u1D441 = 1 uni2211.alt02 . (b) A wheel is divided evenly into 6 different wedges. Each wedge can be painted red (R), white (W), blue (B) or green (G). The back of the wheel is black. We consider two color patterns to be the same (or equivalent) provided one can be obtained from the other by means of a rotation about the center of the wheel. i. What are all of the rotations that make up the symmetry group of this wheel divided into 6 equal parts? List them in the form u1D70C u1D451 where u1D70C u1D451 denotes a coun-...
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4023f10ex3 - Name: Exam 3 Instructions. Answer each of the...

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