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| author | David A. Madore <david+git@madore.org> | 2011-12-22 15:00:22 +0100 |
|---|---|---|
| committer | David A. Madore <david+git@madore.org> | 2011-12-22 15:00:22 +0100 |
| commit | 18585f88389743c30af0be6eeb76d6cd92d9b31f (patch) | |
| tree | 2c2404a0651ad1103df917fe3ed509ae822ea042 /chapitres/calculs-galois.tex | |
| parent | e8b1dd88502d24ae8ce99dd1c6caac68734888b6 (diff) | |
| download | galois-18585f88389743c30af0be6eeb76d6cd92d9b31f.tar.gz galois-18585f88389743c30af0be6eeb76d6cd92d9b31f.tar.bz2 galois-18585f88389743c30af0be6eeb76d6cd92d9b31f.zip | |
[calculs] Diagramme préliminaire pour les sous-groupes transitifs de 𝔖_6.
Diffstat (limited to 'chapitres/calculs-galois.tex')
| -rw-r--r-- | chapitres/calculs-galois.tex | 53 |
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-à -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} |