Unformatted text preview: Determine the elements in each of the following subgroups of the group of symmetries of a square (Table 8.1). (a) h μ 90 i (b) h μ 180 i (c) h μ 270 i (a) μ 2 90 = μ 180 , μ 3 90 = μ 90 μ 180 = μ 270 , μ 4 90 = μ 90 μ 270 = μ . Therefore μ 90 has order 4 and we see that h μ 90 i = { μ , μ 90 , μ 180 , μ 270 } . (b) μ 2 180 = μ . Therefore μ 180 has order 2 and we see that h μ 180 i = { μ , μ 180 } . (c) μ 2 270 = μ 180 , μ 3 270 = μ 270 μ 180 = μ 90 , μ 4 270 = μ 270 μ 90 = μ . Therefore μ 270 has order 4 and we see that h μ 270 i = { μ , μ 90 , μ 180 , μ 270 } . Problem 15.22 page 85 (a) List the elements in the subgroup h ([ 2 ] , [ 2 ]) i of Z 4 × Z 8 . (b) List the elements in the subgroup h [ 2 ] i×h [ 2 ] i of Z 4 × Z 8 . (a) ([0],[0]), ([2],[2]), ([0],[4]), ([2],[6]) (b) ([0],[0]) ([0],[2]) ([0],[4]) ([0],[6]) ([2],[0]) ([2],[2]) ([2],[4]) ([2],[6])...
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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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