Example 13 from Nicholson: Introduction to Abstract Algebra, Section 6.2, page 282 reads as follows: (see attachment)

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Example 13: If show that

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The solution comes down to the following:

Given

so

Now Nicholson shows that and

so

Then Nicholson (I think) concludes that

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My problem is as follows:

How (exactly) does it follow that:

Can someone help?

Peter