To answer how to increase memory, I'm not 100% sure how to do it in Windows if you're using GGAP, but in UNIX you just add, for instance, "-o 1G" to the command you use to start GAP.
On to the bigger question of getting maximal subgroups of S12, using the standard algorithms that GAP has is going to make it quite a challenge. To get maximal subgroups, most of the time GAP will construct the entire subgroup lattice, then work out the inclusions. I should also point out that you might want to run ConjugacyClassesMaximalSubgroups instead of just MaximalSubgroups just to make your output smaller. However, if you need them all, once you get the output of the former, list the classes by the function Elements and then concatenate. The biggest problem here is that S12 is a very, very large group. One of the first functions that GAP will run on this group is Zuppos, which computes conjugacy classes of cyclic subgroups of prime power order. For me, this stalls very badly on S12 (and might not even complete). For the GAP solution, you are in luck as S12 is included in the extended table of marks library available here: http://www.math.rwth-aachen.de/~Thomas.Breuer/tomlib/ Download the file into the pkg directory and extract. Then in GAP run: gap> tom:=TableOfMarks("S12"); TableOfMarks( "S12" ) gap> max:=List(List(MaximalSubgroupsTom(tom)[1]),i->RepresentativeTom(tom,i)); [ <permutation group of size 239500800 with 10 generators>, <permutation group of size 39916800 with 10 generators>, <permutation group of size 7257600 with 10 generators>, <permutation group of size 2177280 with 10 generators>, <permutation group of size 1036800 with 15 generators>, <permutation group of size 967680 with 10 generators>, <permutation group of size 604800 with 10 generators>, <permutation group of size 82944 with 11 generators>, <permutation group of size 46080 with 11 generators>, <permutation group of size 31104 with 11 generators>, Group([ (1,7)(2,10)(3,11)(4,5)(6,8)(9,12), (1,10,4,6,7,9)(2,3,5,8,12,11), (3,6,12,11,7)(4,8,9,5,10), (2,5,3,8,4,9,11,6,12,10,7), (3,4,12,9,7,10,6,8,11,5) ]) ] This gives you conjugacy classes. If you want all of the maximal subgroups, do: gap> G:=UnderlyingGroup(tom); Group([ (1,2), (2,3,4,5,6,7,8,9,10,11,12) ]) gap> allmax:=Concatenation(List(max,i->Elements(ConjugacyClassSubgroups(G,i)))); I'll warn you that one of these classes has size 362880 so this is going to be big. There are a few other ways to get at this, but it involves using the O'Nan Scott theorem. You basically use that (or the ATLAS) to determine the structure of the maximal subgroups and since many of them have a prescribed format you can construct them yourself. Joe On Fri, Jul 15, 2011 at 3:24 PM, Daniela Nikolova < nikolova20032...@yahoo.com> wrote: > Hi folks! > I've just got GAP installed on my new computer under Windows 7, 4GB > memory. I can still not get the maximal subgroups of S_12 - not enough > memory! Please advise me how I can increase the memory. I understand that's > possible under UNIX. > Thanks, > Daniela > > Assoc. Prof. Dr. Daniela Nikolova-Popova > Institute of Mathematics and Informatics, Bulgarian Academy of Sciences > & > Florida Atlantic University, USA > > cell: +1 954 404 3140 > office: +1 561 297 1342 > home: + 359 2 9444 944. > > _______________________________________________ > Forum mailing list > Forum@mail.gap-system.org > http://mail.gap-system.org/mailman/listinfo/forum > _______________________________________________ Forum mailing list Forum@mail.gap-system.org http://mail.gap-system.org/mailman/listinfo/forum
