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4107_midterm1_2008 - Math 4107 exam 1 Each question is...

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Math 4107, exam 1 September 22, 2009 Each question is worth 20 points. 1. Define the following terms. a. Normal subgroup. b. Homomorphism. c. Innerautomorphism. 2. List all the elements of order 2 from the group S 4 . 3. Find integers k and , satisfying 55 k + 21 = 1 , | k | ≤ 20 , | | ≤ 54 . Don’t just write down the answer. Work it using the Euclidean algorithm (e.g. Knuth’s algorithm), so that I know you know some good mathematics. 4. Consider the set of all 2 × 2 matrices of the form bracketleftBigg
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