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Diffstat (limited to 'divers/vrac/sous-groupes-de-s6.dot')
-rw-r--r-- | divers/vrac/sous-groupes-de-s6.dot | 68 |
1 files changed, 68 insertions, 0 deletions
diff --git a/divers/vrac/sous-groupes-de-s6.dot b/divers/vrac/sous-groupes-de-s6.dot new file mode 100644 index 0000000..1f362b7 --- /dev/null +++ b/divers/vrac/sous-groupes-de-s6.dot @@ -0,0 +1,68 @@ +// Compiler avec par exemple: +// dot -Tpng sous-groupes-de-s6.dot -o sous-groupes-de-s6.png +// (le programme dot vient du package graphviz). + +// La numérotation des sous-groupes est celle de Sage(=GAP-1); +// quelques commandes: +// s6 = SymmetricGroup(6) +// lsttrans = [h for h in s6.conjugacy_classes_subgroups() if h.is_transitive()] +// desctrans = [(h.order(),gap.StructureDescription(h),h.is_subgroup(a6)) for h in lsttrans] +// def subgroup_up_to_conjugacy(g,h): +// for x in gap.ConjugateSubgroups(s6,g): +// if gap.IsSubgroup(x,h): +// return True +// return False +// subidx = [[j for j in range(16) if gcd(lsttrans[j].order(),lsttrans[i].order()) == lsttrans[j].order() and subgroup_up_to_conjugacy(lsttrans[i],lsttrans[j])] for i in range(16)] +// maxsubidx = [[j for j in range(16) if is_maximal_subidx(i,j)] for i in range(16)] + +digraph sous_groupes_de_s6 { + g3 -> g0; + g3 -> g1; + g4 -> g0; + g4 -> g1; + g5 -> g1; + g5 -> g2; + g6 -> g2; + g7 -> g0; + g7 -> g2; + g8 -> g3; + g8 -> g4; + g10 -> g3; + g10 -> g5; + g10 -> g6; + g10 -> g7; + g11 -> g2; + g12 -> g8; + g12 -> g9; + g13 -> g3; + g13 -> g7; + g13 -> g11; + g14 -> g6; + g14 -> g9; + g14 -> g11; + g15 -> g10; + g15 -> g12; + g15 -> g13; + g15 -> g14; + g0 [label="S3"]; + g1 [label="C6"]; + g2 [label="A4"]; + g3 [label="D6"]; + g4 [label="S3 × C3"]; + g5 [label="C2 × A4"]; + g6 [label="S4+"]; + g7 [label="S4−"]; + g8 [label="S3 × S3"]; + g9 [label="(C3 × C3) : C4"]; + g10 [label="S4 × C2"]; + g11 [label="A5"]; + g12 [label="(S3 × S3) : C2"]; + g13 [label="S5"]; + g14 [label="A6"]; + g15 [label="S6"]; + g2 [color=blue,fontcolor=blue]; + g6 [color=blue,fontcolor=blue]; + g9 [color=blue,fontcolor=blue]; + g11 [color=blue,fontcolor=blue]; + g14 [color=blue,fontcolor=blue]; +} |