hw22 - . Determine if A is a unit in M 2 ( Z n ) for n = 1...

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Modern Algebra 1 Homework 11.1 Spring 2010 Due April 14 Exercise 1. Express the following permutations as products of transpositions. a. ± 1 2 3 4 5 6 7 8 9 10 3 5 7 1 4 6 10 9 2 8 ² b. ± 1 2 3 4 5 6 7 8 9 10 11 12 1 5 6 7 2 8 9 10 3 11 12 4 ² c. ± 1 2 3 4 5 6 7 8 9 8 7 6 5 1 2 3 4 9 ² Exercise 2. Let A = ± 4 1 3 3
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Unformatted text preview: . Determine if A is a unit in M 2 ( Z n ) for n = 1 , 2 , 3 ,..., 10 and nd its inverse. Exercise 3. Use the correspondence principle to draw the subgroup lattice of Z 84 . [ Hint: Start with the lattice of subgroups of Z that contain h 84 i .]...
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