# Subdomain

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Let p be a prime in Z. Define Z(p) = {m/n in rational Q | p does not divide n}

i) Show that Z(p) is a subdomain of Q

ii) Find the units in Z(p)

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##### Solution Summary

This shows how to prove that a given group is a subdomain.

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Proof:

(1) Z(p) is a subdomain of Q

I only need to show that the addition and multiplication in Z(p) is closed.

For any two elements m/n and s/t in Z(p), we know p does not divide n and p does not divide t. Then we have

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