How do you show that every finite simple group occures as the Galois group of a finite extention of Q?
I ran out of characters. Of course Q is the field of rational numbers.
- Anonymous1 decade agoFavorite Answer
You just made my head explode.
- 1 decade ago
I think you need to look at the fundamental theorem: the subgroups of the Galois group correspond to intermediate fields of the field extension. Being simple means no non-trivial subgroups, so look at the intermediate fields of finite extensions of Q.
The primitive element theorem might also help.Source(s): Wikipedia, plus a vague memory of algebra in grad school.
- firat cLv 41 decade ago
Simple group is not a group with no non-trivial subgroups, it is a group with no non-trivial "normal" subgroups.
- mathematicianLv 71 decade ago
Unless I am mistaken, this is still an open problem.