What is the galois group of $T^3-2$ over $\mathbb{F}_5$?
I dont really see a way to find this group. I saw it for $\mathbb{Q}$ but not $\mathbb{F}_5$.
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3You might start by factoring the polynomial over $\mathbb{F}_5$. – Eric Wofsey Feb 02 '18 at 06:52
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3What stops you from following over ${\bf F}_5$ the steps you took over $\bf Q$? – Gerry Myerson Feb 02 '18 at 08:04
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Any thoughts, Uralmok? – Gerry Myerson Feb 03 '18 at 12:02
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Are you still here, Uralmok? – Gerry Myerson Feb 04 '18 at 22:54
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Hint: Since $2=3^3$ in $\mathbb{F}_5$, the splitting field of $T^3-2$ is the same as the splitting field of $T^3-1$.
lhf
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