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# 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.

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- 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.

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