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Prove that there is no field of order 6.

Prove that there is no field of order 6.
(You can not refer to the fact that all finite field are of prime-power order)

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Proof:
Let F be an fields with order |F|=6. Then we consider its multiplicative group F*=F-{0}.
We know that |F*|=6-1=5 is a prime number and thus F* must be a cyclic group.
We can suppose ...

Solution Summary

It is proven that there is no field of order 6.

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