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Question

Find the order of each element of the group (Z7{[0]},7)

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Solution

G={Z7{[0]}}
={[1],[2],[3],[4],[5],[6]}
The identity element is [1]
O{[1]}=1
O{[2]}=3 since [2]3=1
O{[3]}=6 since [3]6=1
O{[4]}=3 since [4]3=1
O{[5]}=6 since [5]6=1
O{[6]}=2 since [6]2=1

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