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 November 30th, 2017, 02:57 AM #1 Senior Member   Joined: Jan 2015 From: usa Posts: 104 Thanks: 1 subgroups of a Galois group Please help me to answer the following problem: Let $f(x)=x^6+3\in\mathbb{Q}[x]$. Assume the following facts: 1) $f$ is irreducible in $\mathbb{Q}[x]$. Let $\alpha$ be a root of $f(x)$ and $L=\mathbb{Q}(\alpha)$. 2) $L$ is a splitting field for $f(x)$ over $\mathbb{Q}$. 3) $Gal(L/\mathbb{Q})$ is isomorphic to a copy of $S_3$ inside $S_6$. >For each non-trivial proper subgroup $H  December 19th, 2017, 04:22 AM #2 Math Team Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902 Have you determined the possible values of$\displaystyle \alpha$. That is, have you determined all 6 roots of$\displaystyle x^6+ 3= 0\$? Last edited by skipjack; December 19th, 2017 at 07:24 PM. Tags galois, group, subgroups Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post Artus Abstract Algebra 0 May 9th, 2013 05:58 PM goodfeeling Abstract Algebra 2 August 29th, 2012 11:36 AM mathbalarka Abstract Algebra 1 July 11th, 2012 09:34 AM TTB3 Abstract Algebra 6 June 27th, 2009 06:57 AM diondex223 Abstract Algebra 1 March 17th, 2009 08:19 AM

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