What is the Galois group of $x^n + (x-1)^n $ over the rationals in terms of the integer $n$ ? In case that is too hard , what is it for the first 20 integers ?
What is the Galois group of $x^n + (x-1)^n $?
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$\begingroup$
polynomials
galois-theory
pattern-recognition
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0A minor question , what is preferred 'group of f(x)' or 'group of f(x)=0' ? I seem to think the first at least that is what I read all the time. Maybe both are correct ? – 2012-09-19
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0I suppose you mean its Galois Group over the rationals $\mathbb Q$, but you should specify it. Because you know, we could consider its Galois group on every finite field $\mathbb F_q$ as well. – 2012-09-19
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0I am not so familiar with Galois groups over finite fields , plz tell me more or give good link for beginners. I will edit. – 2012-09-19
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2J. Milne's notes on Galois theory are, in my opinion, quite a good material if you're a beginner on the topic. They both covers the theory and the practice, giving many example and a few tricks on how to calculate Galois groups of polinomials over the rationals. Here's the link http://www.jmilne.org/math/CourseNotes/ft.html – 2012-09-19