Question

Let x belong to a group and |x| = 6. Find |x^2|, |x^3|, |x^4|, and |x^5|. Let y belong to a group and |y|=9. Find |y^i| for i=2, 3, ...,8. Do these examples suggest any relationship between the order of the power of an element and the order of the element?

Step 1

Let G be the group, e be the identity element of G and x∈G such that |x|=6 or x^{6}=e which means the order of x is 6.

First, we need to find the order of the elements x^{2}, x^{3}, x^{4} and x^{5}.

Step 2

Now,

Step 3

Again,

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