[GAP Forum] How to increase memory?

[Joe Bohanon]

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 <
nikolova20032003 at 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.
>
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