For each group in the following list find the order of each element in the group:...

For each group in the following list find the order of each element in the group: Z₁₂, U(10) and U(12).

Expert Solution

Please find the solution.

Definition 1: For G an additive group and x?G define the order of x to be the smallest positive integer n such that n.x = Identity of the group, and denote this integer by O(x).

Definition 2: For G a multiplicative group and x?G define the order of x to be the smallest positive integer n such that x^n = Identity of the group, and denote this integer by O(x).

So we will use Definition 1 for Z(12) because Z(12) is an additive group under modulo 12 and '0' is its identity element and Definition 2 for U(10) & U(12) are multiplicative groups under modulo 10 and 12 respectively and '1' is its identity element

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milcah answered 2 years ago

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