Im trying to find a way to connect a possible solution of the inverse Galois problem on simple groups to a more general solution on any finite group.

I've tryied to mess with the embedding problem for a bit but with no success, any help?

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Im trying to find a way to connect a possible solution of the inverse Galois problem on simple groups to a more general solution on any finite group.

I've tryied to mess with the embedding problem for a bit but with no success, any help?

sporadicsimple groups. If memory serves it is still far from solved for all Chevalley groups, and those over the field of $p^n$ elements for $n>1$ tend to be particularly hard. $\endgroup$ – Noam D. Elkies Jun 15 at 17:141more comment