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**JaneFairfax****Member**- Registered: 2007-02-23
- Posts: 6,868

As you know, a finite field always has order a power of a prime. I didnt really know how to prove this until I read Chapter 14 of John F. Humphreyss.

In fact, the result depends on just two results:

**1** is proved by a combination of Lagrange and Sylow. By Lagrange, the order of

**2** comes from the fact that the characteristic of a field is a prime

*Last edited by JaneFairfax (2009-04-21 06:42:57)*

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**JaneFairfax****Member**- Registered: 2007-02-23
- Posts: 6,868

Another result about finite fields is that the multiplicative group of nonzero elements of a finite field is cyclic. This can be proved using a theorem about finite Abelian groups.

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