Dear Gap Forum,

Mario Pineda Ruelas asked:

                          I have GAP 4r2 running on linux RedHat 6.2 on a
Pentium 3 PC with 512MB of RAM and 1 GB of swap memory, and I am trying to
compute the lattice of subgroups of the  group (degree 12): (2,4),
(2,12,10,8,6,4), (9,11),(3,,5,7,11),(1,3,5,7,9,11).

GAP is taking a long time (more than 950 min) to compute this and still has
not finished. I am worried since previously I computed the lattice of
subgroups of a related group of same order and it did not take more than 50
min to do it. For the unfinished computation, when I started GAP I gave it
the following memory parameters: -m 500m -o 1000m.
My question is: Could it be that GAP has fallen into an infinite loop?

I don't think it has. The time needed to compute the full lattice depends
not only on the size of the group but also its structure. In particular
a large number of subgroups tends to slow down the calculation.

If you want a progress report of the calculation, you can set
SetInfoLevel(InfoLattice,n);
where n=1 or n=2 (n=0 to turn off again) and GAP will tell you how far it
is in the computation.

The group in your example is S6xS6. Due to this direct product structure
there will be a large number of elementary abelian subfactors.
(On the other hand it is not too hard to parametrize the subgroups of AxB as
subdirect products of subgroups of A and B, and it might be possible to
find the information you look for this way.)

I did not run your example through to the bitter end, but after a few
minutes it had already defined thousand subgroup classes and was still only
considering subgroups of size 8. (I then took pity with the poor computer
slaving away on what looked like a very long task and stopped the
calculation.)

Best regards,

Alexander Hulpke

-- The Ohio State University, Department of Mathematics,
231W 18th Avenue, Columbus, OH 43210, USA
email: ahulpke@math.ohio-state.edu, Phone: ++1-614-688-3175