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Let G be a group of odd order. Prove that the mapping x x2

Chapter 11, Problem 16SE

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QUESTION:

Let G be a group of odd order. Prove that the mapping \(x \rightarrow x^2\) from G to itself is one-to-one.

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QUESTION:

Let G be a group of odd order. Prove that the mapping \(x \rightarrow x^2\) from G to itself is one-to-one.

ANSWER:

Step 1 of 3

Suppose that . This means that for all  we have .

Let  be such that .

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