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authorDavid A. Madore <david+git@madore.org>2011-12-22 14:00:22 (GMT)
committerDavid A. Madore <david+git@madore.org>2011-12-22 14:00:22 (GMT)
commit18585f88389743c30af0be6eeb76d6cd92d9b31f (patch)
tree2c2404a0651ad1103df917fe3ed509ae822ea042 /chapitres/calculs-galois.tex
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[calculs] Diagramme préliminaire pour les sous-groupes transitifs de 𝔖_6.
Diffstat (limited to 'chapitres/calculs-galois.tex')
-rw-r--r--chapitres/calculs-galois.tex53
1 files changed, 53 insertions, 0 deletions
diff --git a/chapitres/calculs-galois.tex b/chapitres/calculs-galois.tex
index 766eb3e..12a8c7b 100644
--- a/chapitres/calculs-galois.tex
+++ b/chapitres/calculs-galois.tex
@@ -14,6 +14,7 @@
\usepackage{tikz}
\usetikzlibrary{matrix}
\usetikzlibrary{calc}
+\usetikzlibrary{positioning}
\usepackage{srcltx}
\externaldocument{corps-finis}
@@ -2665,6 +2666,58 @@ relative). Si $G$ est contenu dans les deux, c'est-Ă -dire dans $D_5 =
contenu dans $C_5$ comme on vient de l'indiquer.
+\subsection{Degré $6$}
+
+\begin{center}
+\begin{tikzpicture}[auto,node distance=5ex and 3em]
+\node (group-15) {$\mathfrak{S}_6$};
+\node (group-14) [below=of group-15] {$\mathfrak{A}_6$};
+\node (group-10) [right=of group-14] {$\mathfrak{S}_4 \times C_2$};
+\node (group-13) [right=of group-10] {$\mathfrak{S}_5$};
+\node (group-12) [left=of group-14] {$(\mathfrak{S}_3\times\mathfrak{S}_3):C_2$};
+\node (group-6) [below=of group-14] {$\mathfrak{S}_4^+$};
+\node (group-11) [right=3.5em of group-6] {$\mathfrak{A}_5$};
+\node (group-5) [right=of group-11] {$\mathfrak{A}_4 \times C_2$};
+\node (group-7) [right=of group-5] {$\mathfrak{S}_4^-$};
+\node (group-9) [left=of group-6] {$(C_3\times C_3):C_4$};
+\node (group-8) [left=of group-9] {$\mathfrak{S}_3 \times \mathfrak{S}_3$};
+\node (group-3) [below=of group-6] {$D_6$};
+\node (group-2) [right=of group-3] {$\mathfrak{A}_4$};
+\node (group-4) [left=4em of group-3] {$\mathfrak{S}_3 \times C_3$};
+\node (group-1) [below=of group-3] {$C_6$};
+\node (group-0) [right=of group-1] {$\mathfrak{S}_3$};
+\draw (group-15) -- (group-14);
+\draw (group-15) -- (group-10);
+\draw (group-15) -- (group-13);
+\draw (group-15) -- (group-12);
+\draw (group-14) -- (group-9);
+\draw (group-14) -- (group-6);
+\draw (group-14) -- (group-11);
+\draw (group-10) -- (group-6);
+\draw (group-10) -- (group-5);
+\draw (group-10) -- (group-7);
+\draw (group-10) -- (group-3);
+\draw (group-13) -- (group-11);
+\draw (group-13) -- (group-7);
+\draw [out=225,in=30] (group-13) to (group-3);
+\draw (group-12) -- (group-8);
+\draw (group-12) -- (group-9);
+\draw (group-6) -- (group-2);
+\draw (group-11) -- (group-2);
+\draw (group-5) -- (group-2);
+\draw [out=270,in=45] (group-5) to (group-1);
+\draw (group-7) -- (group-2);
+\draw (group-7) -- (group-0);
+\draw (group-8) -- (group-4);
+\draw (group-8) -- (group-3);
+\draw (group-3) -- (group-1);
+\draw (group-3) -- (group-0);
+\draw (group-4) -- (group-1);
+\draw (group-4) -- (group-0);
+\end{tikzpicture}
+\end{center}
+
+
\ifx\danslelivre\undefined
\bibliography{../configuration/bibliographie-livre}