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Unverified Commit 67274a5c authored by rrueger's avatar rrueger
Browse files

Algebra II: Lecture 6. Grammar/Readability

parent 8aa090b4
......@@ -106,7 +106,7 @@ will find that the answer to both of these questions is yes. Define $E = \C(X_1,
If we now look at the action of $S_n$ on $\{X_1, \ldots, X_n \}$, with $\sigma
\in S_n$ acting by $\sigma(X_i) = X_{\sigma (i)}$ we see that $\sigma(e_k) =
e_k$, $S_n$ poses a good candidate for the automorphism group as a group
e_k$. So $S_n$ poses a good candidate for the automorphism group as a group
action. In particular, we know that the $e_k$'s form a basis of $F$, thus we
know that $S_n$ fixes $F$, and hence must be a subset of the automorphism
group. Of course however $|S_n| = n!$ and thus $S_n = \Aut(E/F)$. Finally we
......
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