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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 90 i (b) h 180 i (c) h 270 i (a) 2 90 = 180 , 3 90 = 90 180 = 270 , 4 90 = 90 270 = . Therefore 90 has order 4 and we see that h 90 i = { , 90 , 180 , 270 } . (b) 2 180 = . Therefore 180 has order 2 and we see that h 180 i = { , 180 } . (c) 2 270 = 180 , 3 270 = 270 180 = 90 , 4 270 = 270 90 = . Therefore 270 has order 4 and we see that h 270 i = { , 90 , 180 , 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 ] ih [ 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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 Fall '08
 PARRY
 Math, Algebra

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