[GAP Forum] How can I extend the "permitted memory"?

[Joe Bohanon]

Oliver and Forum,

Here is how you can get what you want without StructureDescription (and 
which I highly recommend for big groups):

Oliver's group was generated by

I20:=(1,2,4,8,16,11)(3,6,12)(5,10,20,19,17,13)(7,14)(9,18,15);
O20:=(2,3,5,9,17,14,8,15,10,19,18,16,12,4,7,13,6,11);

First off, given that this is a shuffle group, the structure is well 
known and can be found here:

http://uoregon.edu/~kantor/PAPERS/PerfectShuffles.pdf

The answer to his question is that this group has the form Z2^10 : S10 
or also the wreath product S2 wr S10.

However, to show how this can be achieved in GAP, first a brief 
description of what StructureDescripton does.  Basically, you want to 
find normal subgroups that tell a lot about the structure of G.  For 
every one you find, you can say something about G, but finding the best 
one is a bit difficult.  When you call StructureDescription it first 
tries to determine if you have a "nice" group, where "nice" is anything 
like "abelian", "dihedral", "simple", "symmetric" etc.  GAP has no 
trouble recognizing gigantic groups if they fall in one of those 
categories.  It can also easily find if you have a direct product.  
Beyond that it essentially tries to compute the entire lattice using a 
call to ConjugacyClassesSubgroups.  When you call that, the newest 
version of GAP first finds the solvable radical S (the largest solvable 
normal subgroup) and computes the lattice of G/S.  In this case, you had 
S10.  For groups without a solvable radical, it uses 
"LatticeByCyclicExtension", which starts with a call to "Zuppos" which 
was the first place the call to StructureDescription gets bogged down.  
The zuppos are cyclic subgroups of prime power order, of which there are 
344,251 in S10.  I've seen GAP compute zuppos that high before, but it 
takes quite a while.  GAP will use these to build the entire lattice 
from the bottom up.  After this completes (and for S10, it might not, 
unless you have a ton of memory), it pulls the subgroups it find back to 
G, and tries to figure out, for each pre-imaged subgroup of S10, which 
subgroups of 2^10 are invariant under it.  That's the second huge 
problem with this group as 2^10 has gobs and gobs of subgroups.

So here's how I would approach this problem once I knew the size of the 
group was too big to use StructureDescription for.

gap> N:=RadicalGroup(G);
<permutation group of size 1024 with 10 generators>
gap> StructureDescription(last);
"C2 x C2 x C2 x C2 x C2 x C2 x C2 x C2 x C2 x C2"
gap> StructureDescription(G/N);
"S10"

At this point, I know the group has the form Z2^10 . S10, but now I need 
to know if it splits or not.  In this case, since N is solvable, I can run

gap> Complementclasses(G,N);
[ <permutation group with 19 generators>, <permutation group with 19 
generators> ]

This says that GAP found what we need, so this is a split extension.  If 
it returned [] we'd know it was non-split.

If you're dealing with a different groups where N is not solvable, 
things are considerably more difficult.  The best solution I can come up 
with is to run IsomorphicSubgroups(G,G/N), but many times this involves 
calling StructureDescription, which I wanted to avoid in the first 
place.  However, if G/N is small enough you might avoid that problem.

Hope this helps
Joe


chakachak wrote:
> That is very kind of you!
>
>
> Here are the two generators:
>
> I20:=(1,2,4,8,16,11)(3,6,12)(5,10,20,19,17,13)(7,14)(9,18,15);
> O20:=(2,3,5,9,17,14,8,15,10,19,18,16,12,4,7,13,6,11);
>
> It´s for my paper I need to write for my Examination. I am writing 
> about shufflegroups.
>
> Thank You very, very much!
>
> Yours Oliver Benjamin from Cologne.
>
>
>
>
> Am 21.03.2010 um 12:29 schrieb Joe Bohanon:
>
>> My guess is that with a group of that size, you stand no chance of 
>> getting an answer out of StructureDescription even with a lot of memory.
>>
>> That said, send me the generators in a separate e-mail and I'll try 
>> it out on a machine with 4 GB of RAM.  I might also be able to get 
>> you a StructureDescription without using that function.
>>
>> Joe
>>
>> chakachak wrote:
>>> Hello GAP-Forum,
>>>
>>> I am new to GAP and I have a question concerning the "-o command 
>>> line option".
>>>
>>> When I am giving GAP the StructureDescription-Command on a Group of 
>>> order 3715891200 after half an hour or so GAP says:
>>>
>>> "exceeded the permitted memory (`-o' command line option)"
>>>
>>> As a MacBook-User I can´t do anything with the suggestions from the 
>>> ReferenceManual: Whatever suggested key I pressed while opening GAP, 
>>> I  did not accomplish to open the dialog box in which I should write 
>>> the command the extend the workspace. And even if I would accomplish 
>>> to open the dialog box, the ReferenceManual says, that as a 
>>> MacOs-User it would be impossible to change the Workspace over the 
>>> -o command line option...
>>>
>>> So:
>>>
>>> How can I expand the workspace?
>>>
>>>
>>> Thanks in advance
>>>
>>> from Oliver Benjamin from Cologne in Germany.
>>>
>>>
>>>
>>>
>>>
>>>
>>>
>>>
>>> _______________________________________________
>>> Forum mailing list
>>> Forum at mail.gap-system.org
>>> http://mail.gap-system.org/mailman/listinfo/forum
>>>
>
>