Can the multiplicative group of a finite field be proven to be cyclic?

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SUMMARY

The multiplicative group of a finite field F, denoted as F*, is proven to be cyclic. Given that the order of the finite field F is n, the order of the multiplicative group is m = n - 1. This implies that for any element g in F*, the equation g^m = 1 holds true. The cyclic nature of F* can be established through group theory principles, specifically leveraging the properties of finite fields.

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dogma
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Letting F be a finite field, how would one show that the multiplicative group must be cyclic?

I know that if the order of F = n, then the multiplicative group (say, F*) has order n - 1 = m. Then g^m = 1 for all g belonging to F*.

Thanks for your time and help.

dogma
 
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google for multiplicative group finite field cyclic, and look at the first hit from planetmath
 
thank you once again...google is great.

dogma
 

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