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Unverified Commit 9b6a51b9 authored by rrueger's avatar rrueger
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Algebra II: Lecture 6. Remark on definition of \Z_2

parent 67274a5c
......@@ -162,9 +162,9 @@ look at the subgroups of the Galois group (Part 1 of F.T.G.T).
\begin{align*}
\set{\id}
\triangleleft \Z_2
\triangleleft A_n
\triangleleft A_4
\triangleleft K_4
\triangleleft S_n
\triangleleft S_4
\end{align*}
%
with
......@@ -187,6 +187,13 @@ look at the subgroups of the Galois group (Part 1 of F.T.G.T).
%
so we have a tower of extensions that are all Galois each corresponding to a
subgroup $\Z_2, K_4, A_4, S_4$.
%
\begin{remark}
Of course in general $\Z_2 = \set{\id, (12)} \cong \set{\id, (12)(34)}
\subseteq S_4$, however to aid notation, we simply write $\Z_2 = \set{\id,
(12)(34)}$. Otherwise $\set{\id, (12)} \not\leq K_4$ (it's not even a
subset).
\end{remark}
\end{example}
\subsection{Solvability of the General Equation}
......
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