I have quoted a very old message of yours from forum which is; -quoted text starts here- Once you computed the subgroup lattice, other commands help you to find out more about it. An Example is "MaximalSubgroups". Let's see how this works on your example:
gap> g:=SymmetricGroup(3);; gap> lat:=LatticeSubgroups(g); <subgroup lattice of Sym( [ 1 .. 3 ] ), 4 classes, 6 subgroups> gap> classes:=ConjugacyClassesSubgroups(lat); [ Group( () )^G, Group( [ (2,3) ] )^G, Group( [ (1,2,3) ] )^G, SymmetricGroup( [ 1 .. 3 ] )^G ] gap> lengths:=List(classes, Size); [1, 3, 1, 1 ] # Hence the lattice has 4 conjugacy classes, one of length 3 and 3 of # length 1. These are three normal subgroups! # Now we take representatives in the classes... gap> repr:=List(classes, Representative); [ Group(()), Group([ (2,3) ]), Group([ (1,2,3) ]), Sym( [ 1 .. 3 ] ) ] gap> sizes:=List(repr, Size); [ 1, 2, 3, 6 ] # OK. Now we know the groups in our classes. gap> maxsg:=MaximalSubgroupsLattice(lat); [ [ ], [ [ 1, 1 ] ], [ [ 1, 1 ] ], [ [ 3, 1 ], [ 2, 1 ], [ 2, 2 ], [ 2, 3 ] ] ] # Here we see that the groups in the first class have no subgroups. Of # course! The groups in that class are trivial. # A representative of the second class contains a group of the first class # as a maximal subgroup. The same is true for a representative of the # third class. A representative of the fourth class (i.e. the group Sym(3) # itself) contains the group of the third class and all three groups of # the second class as maximal subgroups. With this information you can make a picture of the subgroup lattice of Sym(3). More commands like this are available in GAP: just check the manual. As an exercise, you should try the command "MinimalSupergroupsLattice". I have some experience with subgroup lattices in GAP. If you need more information, I'll be happy to help you. Some years ago, I wrote a program which generates a LaTeX file with the subgroup lattice of a given group in the form of a table. This enables you to work in the subgroup lattice if needed. If you really want a picture, you should take a look at xgap but beware that subgroup lattices rapidly become very complicated and difficult to draw. -quoted text finishes here.- can anyone give some information about that program which generates a LaTeX file with the subgroup lattice of a given group in the form of a table. OR, actually, I use windows xp installed on my computer, thus I am not able to use XGAP. but I want to see a picture of the lattice of subgroups of a group, namely a picture of which subgroup is contained in which subgroup. GAP turns out lists, which are not very helpful in this way. can anyone help me? -- *Sümeyra Bedir* _______________________________________________ Forum mailing list Forum@mail.gap-system.org http://mail.gap-system.org/mailman/listinfo/forum
