Let G be the Galois group of the splitting field of $(x^p)-2$ over Q, where p is odd prime , Then which of the following are correct? (1) G has an element of order 4 if $p=5$. (2) G has an element of order $p-1$. (3) G is non abelian. (4) G is abelian for some $p$.
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2There are no finite fields in this question. – lulu Apr 12 '18 at 12:50
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1It's a good idea to start with examples. You can read about $x^3-2$ here. – lulu Apr 12 '18 at 12:51
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$x^p-2$ or $x^{p-2}$ ? – user577215664 Apr 12 '18 at 13:29
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1$x^{p-2}$ is trivial, @Isham – Guillermo Mosse Apr 12 '18 at 14:11
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I edit it so please see it again. – Poonam Bai Apr 12 '18 at 14:14
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Calling this a duplicate of this older one. This question also looks like a copy/pasted homework problem. Suggesting closure. – Jyrki Lahtonen Apr 12 '18 at 14:27
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I agree that this question may be similar to a problem that is discussed previously but this is a different one. – Poonam Bai Apr 12 '18 at 22:33
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If it is duplicate then what are correct options of above question? Please help. – Poonam Bai Apr 18 '18 at 11:03