What is the Galois group of a polynomial over a finite field?
Here are 14 best answers to ‘What is the Galois group of a polynomial over a finite field?’  the most relevant comments and solutions are submitted by users of Mathematics, Yahoo! Answers and Quora.
Related Questions & Answers
 What are the main differences between a Mobile and a PDA?
 What happens to the temperature of a substance during a phase change?
 How is dividing a polynomial by a binomial similar to or different from the long division?
 Currently produced in a wire in a magnetic field?
 Interview for a job in a different field?
Best solution

What is the Galois group of the splitting field of $X^83$ over $\mathbb{Q}$?
I've computed the splitting field of $x^83$ over $\mathbb{Q}$ to be $\mathbb{Q}(\sqrt[8]{3},\zeta_8)=\mathbb{Q}(\sqrt[8]{3},\sqrt{2},i)$, which is of degree 32 over $\mathbb{Q}$. The possible automorphisms are the maps fixing $\mathbb{Q}$ of form $$ \sqrt[8]{3}\mapsto \zeta_8^i\sqrt[8]{3}\quad (0\leq i\leq 7),\qquad \sqrt{2}\mapsto\pm\sqrt{2},\qquad i\mapsto\pm i. $$ There are 32 automorphisms, and thus these are all automorphisms. So I have an explicit description of the automorphisms in the...
Answer:
Your description of $G$ is perfectly fine as it is. But maybe a representation of $G$ in $GL_2(\mathbb...
Other solutions

What is the Galois group for splitting field Q[sqrt(2)+sqrt(3)]?
Answer:
Klein 4group. (This field is already Galois over the rational numbers.)

Answer:
The fixed field is also Galois.

Are group theory, field theory, Galois theory or category theory useful in theoretical economics?
For example, Galois connections have made an appearance in a recent paper on implementation by Noldeke and Samuelson: Page on wiso.tudortmund.de.
Answer:
In the context of that paper, a "Galois connection" simply refers to an orderreversing correspondence...

Abstract Algebra: Galois Theory construction for a polynomial HELP?
I've basically constructed the automorphisms for f(x) = (x^2  2)(x^2  3), however I need to find the Galois group. Does anyone know how to do this? I turned in my work to the professor but I wasn't sure if my solution is complete. I have the following...
Answer:
Since both Q(√2) and Q(√3) are subfields of Q(√2, √3), the automorphisms of...

Enter a group address in the bcc field how can I remove only one addresss from the group addres?
I tried the answer that I was given by an other person on Yahoo. Problem is when I select my group it enters the name of the group in the BCC field and there are no individual addresses to remove. Can you give me other answers See below
Answer:
Give this yahoo tech. group a try... http://tech.groups.yahoo.com/group/Compu… Or these people...

Enter a group address in the bcc field how can I remove only one address from the group addres?
For Exp. I enter a group address from my address book in the to field. Then I want to remove "Jerry" email address only because he sent me the original email. How can I remove him only and sent the email to the rest of the group
Answer:
Once you click on the group you want to blind copy, the names in the group should appear. When you see...

I got put in a weird awkward field trip group?
I just checked the groupings, and all of my friends literally, were put in one group and the teacher didn't include me in it..instead, he put me in a group with people i never talk to & people who freak me out a little o.0 as in, some of these people...
Answer:
Keep an open mind. Use the experience to get out of your comfort zone, you may end up making a friend...

Index of Splitting Field (galois Theory)?
Suppose that the polynomial ax^4 + bx^2 + c for some a,b,c in Q (rationals) is irreducible over Q and let K be a splitting field over Q for it. Prove that [K:Q] is either 4 or 8. I'm trying to work through the different cases of the roots of the polynomial...
Answer:
When you adjoin one root r then you get an extension of degree 4. Now either this is the splitting field...

Since most fields have several people whose separate contributions have shaped that field, this question is about weighing which single person out of those several had the greatest contribution according to you, and why?
Answer:
In my field, it would probably be William Kennedy Laurie Dickson, though chances are early incarnations...