Find the order of every element in Z18SolutionAll subgroups

Find the order of every element in Z_18.

All subgroups of Z18: there is exactly one for each divisor of 18.

The subgroups are <1> = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17},

<2> = {0, 2, 4, 6, 8, 10, 12, 14, 16},

<3> = {0, 3, 6, 9, 12, 15},

<6> = {0, 6, 12},

<9> = {0, 9} and

<0> = {0}.

$Find the order of every element in Z_18.SolutionAll subgroups of Z18: there is exactly one for each divisor of 18. The subgroups are <1> = {0, 1, 2, 3, 4$

Find the order of every element in Z18SolutionAll subgroups

Solution

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