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authorDavid A. Madore <david+git@madore.org>2011-12-22 13:03:17 (GMT)
committerDavid A. Madore <david+git@madore.org>2011-12-22 13:03:17 (GMT)
commite8b1dd88502d24ae8ce99dd1c6caac68734888b6 (patch)
treedb5cef346b31f8fb6a81ab1538dd81c2c69b90eb
parent0c8388f79921491dcede3256e3c54a0df75cbfce (diff)
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sageries: noms des sous-groupes de 𝔖_6
-rw-r--r--divers/sageries/sous-groupes-s62
1 files changed, 2 insertions, 0 deletions
diff --git a/divers/sageries/sous-groupes-s6 b/divers/sageries/sous-groupes-s6
index 9c4b449..a8a1cc6 100644
--- a/divers/sageries/sous-groupes-s6
+++ b/divers/sageries/sous-groupes-s6
@@ -1,6 +1,8 @@
s6 = SymmetricGroup(6)
tuplegens = [[[(1, 4), (2, 3), (5, 6)], [(1, 5, 3), (2, 6, 4)]], [[(1, 4), (2, 5), (3, 6)], [(1, 5, 3), (2, 6, 4)]], [[(2, 5), (3, 6)], [(1, 4), (2, 5)], [(1, 6, 5), (2, 4, 3)]], [[(2, 6), (3, 5)], [(1, 4), (2, 5), (3, 6)], [(1, 5, 3), (2, 6, 4)]], [[(2, 6, 4)], [(1, 4), (2, 5), (3, 6)], [(1, 5, 3)]], [[(3, 6)], [(2, 5)], [(1, 4)], [(1, 6, 5), (2, 4, 3)]], [[(2, 3), (5, 6)], [(2, 5), (3, 6)], [(1, 4), (2, 5)], [(1, 6, 5), (2, 4, 3)]], [[(2, 5), (3, 6)], [(2, 6, 5, 3)], [(1, 4), (2, 5)], [(1, 6, 5), (2, 4, 3)]], [[(2, 6, 4)], [(2, 6), (3, 5)], [(1, 4), (2, 5), (3, 6)], [(1, 5, 3)]], [[(2, 6, 4)], [(2, 6), (3, 5)], [(1, 4), (2, 3, 6, 5)], [(1, 5, 3)]], [[(3, 6)], [(2, 3), (5, 6)], [(2, 5)], [(1, 3, 5), (2, 4, 6)], [(1, 4)]], [[(1, 4), (2, 6)], [(1, 5, 3, 4, 6)]], [[(4, 6)], [(3, 5)], [(2, 6, 4)], [(1, 4), (2, 5), (3, 6)], [(1, 5, 3)]], [[(2, 3, 4, 6)], [(1, 2, 3, 6, 4)], [(1, 6), (4, 5)]], [[(2, 6, 4)], [(1, 5, 3, 4, 2)]], [[(1, 2, 3, 4, 5, 6)], [(1, 2)]]]
groups = [s6.subgroup(l) for l in tuplegens]
+a6 = [h for h in groups if h.order()==360][0]
+groupdesc = [(h.order(), gap.StructureDescription(h), h.is_subgroup(a6), s6.order()/s6.normalizer(h).order()) for h in groups]
alsocontains = [(4, 0), (11, 2), (13, 2), (13, 7)]
strictcontains = [(i,j) for i in range(16) for j in range(16) if groups[j].is_subgroup(groups[i])]
contains = [(i,j) for i in range(16) for j in range(16) if (i,j) in strictcontains or (i,j) in alsocontains]