Is G isomorphic to the Galois group of a polynomial in Q?

[futurebird]

Given a finite group G is G isomorphic to the Galois group of some polynomial in Q? Having done a course on Galois theory I think I just missed this and I feel like I ought to know the answer. Did I just sleep through that part of class?

:/

 

[HallsofIvy]

Given a finite group G is G isomorphic to the Galois group of some polynomial in Q? Having done a course on Galois theory I think I just missed this and I feel like I ought to know the answer. Did I just sleep through that part of class?

:/

That's not a question. Given that a finite group G is isomorphic to the Galois group of some polynomial, what? What conclusion are you to make?

 

[Dunkle]

I think what the question is asking is the following. If you are given some finite group, is it isomorphic to the Galois group of some polynomial in Q?

 

[futurebird]

I'm asking if for every finite group is there at least one polynomial in Q that has that group as its Galois group.

That is we did a lot of "give a polynomial find the Galois group." can you do always the reverse?

maybe this is obvious or something...

 

[futurebird]

I think what the question is asking is the following. If you are given some finite group, is it isomorphic to the Galois group of some polynomial in Q?

Yes. This is just the question.

 

[Dick]

That's the Inverse Galois Problem. You can search online for info. I don't think the answer is completely known.

 

[futurebird]

Thanks! It looks pretty cool.