1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
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];
}
|
