Can someone help me in establishing an image of how the group looks like. I am having a hard time visualizing it.
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Just as finite extensions of $\mathbb{Q}$ are basically $\mathbb{Q}^n$ with defined multiplications (corresponding to the minimal polynomial the generator satisfies), $\mathbb{F}_{p^n}$ is basically $\mathbb{F}_p^n$ with defined multiplications. – fretty Apr 08 '14 at 08:00
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Here the elements of $GF(4)$, $GF(8)$ and $GF(16)$ are listed together with examples of arithmetic operations in those fields. Hope that helps. – Jyrki Lahtonen Apr 08 '14 at 08:05
