Midterm - Takehome Midterm Math 332, Spring 2010 This...

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Unformatted text preview: Takehome Midterm Math 332, Spring 2010 This midterm has six problems, each of which has several parts. Your solutions must be written up in L A T E X, and are due on Friday, April 30. Late solutions will not be accepted. Because this is a midterm, you are required to solve these problems on your own. Please do not discuss the solutions with any other students. If you are having trouble, feel free to e-mail me a question, or come to my office hours sometime over the next two weeks. 1. The dicyclic group Dic 3 is a certain nonabelian group of order 12. It consists of the elements { e, a, a 2 , a 3 , a 4 , a 5 , b, ab, a 2 b, a 3 b, a 4 b, a 5 b } , where a and b satisfy the following relations: a 6 = e, b 2 = a 3 , and ba = a- 1 b. (a) Determine the orders of the elements of Dic 3 . Use your answer to prove that Dic 3 is not isomorphic to D 6 or A 4 . (b) Find a normal subgroup N C Dic 3 of order 2, and determine the isomorphism type of Dic 3 /N ....
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Midterm - Takehome Midterm Math 332, Spring 2010 This...

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