My Math Forum Extension Fields/Galios

 Abstract Algebra Abstract Algebra Math Forum

 April 29th, 2009, 12:25 AM #1 Member   Joined: Dec 2007 Posts: 43 Thanks: 0 Extension Fields/Galios f degree n poly over Q K the splitting field of f Gal(K/Q) isomorphic to $S_n$ a. proved f irreducible since if it were, [K:Q]2 and $\alpha$ a root of f(x) in K, show $Aut(Q(\alpha)/Q)=1$ i claimed that since [K:Q]=n!, then K must be a separable extension since f deg n so [K:Q] is the largest it can be ... then roots go to roots and there is only on root in Q(a) so we're done. is this right? c. if $n \geq 4$ show that $\alpha ^n \notin Q$ not really sure how to start this one any nudges in the right direction are greatly appreciated.

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post Tom19 Abstract Algebra 2 November 13th, 2013 05:20 AM Sandra93 Abstract Algebra 4 November 12th, 2013 03:21 AM Generic Abstract Algebra 1 April 1st, 2012 03:25 PM Scooter Number Theory 1 October 19th, 2010 08:08 PM goodfeeling Algebra 0 December 31st, 1969 04:00 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top