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Unformatted text preview: 4. Problem 16.2 on page 87. Determine the right cosets of h [ 3 ] i in Z 12 . { [0], [3], [6], [9] } { [1], [4], [7], [10] } { [2], [5], [8], [11] } 5. Problem 16.17 on page 88. Compute the right cosets of h (( 1 2 ) , [ 1 ]) i in S 3 Z 2 . Let H = h (( 1 2 ) , [ 1 ]) i . Then H = { (( 1 ) , [ ]) , (( 1 2 ) , [ 1 ]) } , a subgroup of order 2. Since the order of S 3 Z 2 is 6 * 2 = 12, we expect 12/2 = 6 cosets. The cosets are H (( 1 ) , [ ]) = { (( 1 ) , [ ]) , (( 1 2 ) , [ 1 ]) } H (( 2 3 ) , [ ]) = { (( 2 3 ) , [ ]) , (( 1 2 3 ) , [ 1 ]) } H (( 3 1 ) , [ ]) = { (( 3 1 ) , [ ]) , (( 1 3 2 ) , [ 1 ]) } H (( 1 2 ) , [ ]) = { (( 1 2 ) , [ ]) , (( 1 ) , [ 1 ]) } H (( 1 2 3 ) , [ ]) = { (( 1 2 3 ) , [ ]) , (( 2 3 ) , [ 1 ]) } H (( 1 3 2 ) , [ ]) = { (( 1 3 2 ) , [ ]) , (( 1 3 ) , [ 1 ]) }...
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This note was uploaded on 01/02/2012 for the course MATH 3124 taught by Professor Parry during the Fall '08 term at Virginia Tech.
 Fall '08
 PARRY
 Math, Algebra

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