Suppose $E/F$ is Galois extension. What is it known about structure of $F[Gal(E/F)]$?
I've learned only one fact in this direction - existence of normal basis in $E/F.$ But it's not truly about $F[Gal(E/F)].$
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Hmm, I wonder, is there something nice that can be said about $F[G_{E/F}]$ that doesn't derive from results on group algebras in general? [i.e. something structure-theoretic that distinguishes these group algebras from others] – anon Dec 14 '13 at 06:52
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@anon: Now I'm reading your answer to the similar question: http://math.stackexchange.com/a/470572/67230 ) – ptashek Dec 14 '13 at 06:57