Quiz2Solutions

Quiz2Solutions - Math 332 Spring 2010 Quiz Name 1[8 points...

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Math 332, Spring 2010 Name: __________________________________ Quiz # 1. Let be the group of integers under addition, and let be the group [8 points] Z Z K À + − " + ! " œ under the operation of matrix multiplication. Prove that is isomorphic to . K Z
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2. Consider the following subgroup of : [8 points] ^ ‚ ^ ' $ L œ e f a b a b a b a b a b a b . Determine the cosets of in . (That is, list the elements in each of the three cosets.) L ^ ‚ ^ ' $ 3. Let Aut , and suppose that and . Express as a permutation c d 8 points ! ! ! ! H < œ < = œ <= a b a b a b # of the elements of the set . e f /ß <ß < ß < ß < ß =ß <=ß < =ß < =ß < = # $ % # $ %
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4. [6 points (3 pts each)] (a) Determine the isomorphism type of . Express your answer as a direct product of cyclic a b groups. (b) Compute mod . # 5. Find an element of order in . [6 points] W ‚ ^ "!
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Quiz2Solutions - Math 332 Spring 2010 Quiz Name 1[8 points...

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