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.
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