[GAP Forum] StructureDescription & memory
Steve Linton
sal at cs.st-and.ac.uk
Tue Apr 8 15:38:22 BST 2008
A partial answer:
As you observe, these groups are all of rank 7. I think they can be understood
as D8 x C_2^5, Q8 x C_2^5, and 2^{1+4}_+ x C_2^3 and 2^{1+4}_- x C_2^3,
although I haven't checked this fully.
The first step in computing the structure description is to list the normal
subgroups of the group, and the essential problem is that these groups have
very many normal subgroups.
I don't know exactly what computing the structure description involves in
general, so I'm not sure if it the normal subgroup computation can be avoided
in general, but most interesting questions about the groups (upper and lower
central series, for instance) can be answered very quickly using standard GAP
functionality.
Steve
On Tue, 8 Apr 2008 09:42:30 -0400
"R. Keith Dennis" <dennis at rkd.math.cornell.edu> wrote:
>
> Over the past year I've been doing a large number of computations
> with GAP and as I require much of the same data to be computed
> over & over again, I've been storing it. One of the items I've
> been storing is the StructureDescription of a large number of
> groups. I realize that for groups, especially p-groups, the
> information obtained isn't always that useful, but sometimes it is.
> For more complicted groups (lots of factors in the order) this
> seems to be very expensive to compute, and very slow (hence the
> reason to store it).
>
> I've run into a problem, which may be intrinsic to the problem, may
> be a problem with gap, or might be a problem with our computer or
> operating system. Perhaps someone can tell me which.
>
> Ok, a perhaps stupid computation, but let's ignore that part:
> I've computed the structure descriptions of all the groups of order
> 256 (56092 total) except for the ones numbered 56083 through 56087. I
> believe all of these are of rank 7. I've now either run out of memory
> and had GAP quit, or I've brought the machine down 3 times when trying
> to compute the result for 56083 or 56087. With memory set at a max of
> 50G the computation runs out of memory and quits. I've tried 100G and
> 80G with the same result - a crash. The machine does have 128G of ram
> and several times that in swap space (as well as 16 CPUs).
>
> Any ideas what the problem may be?
>
>
> One further question and a remark:
>
> Are there any other implementations of a computation of structure
> description that gives more useful information that that in gap?
>
>
> I still believe that it makes sense to have a community accessible
> archive of many such "standard" computations as structure
> descricption, although when I raised that question at the recent
> computational group theory conference in Ohio, there was not a great
> deal of enthusiasm for the idea. With the current cheap price of
> storage (especially compared to that of memory and the time expended
> for comutation), it would seem to make sense, to me at least.
>
>
> Keith
>
>
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--
Steve Linton School of Computer Science &
Centre for Interdisciplinary Research in Computational Algebra
University of St Andrews Tel +44 (1334) 463269
http://www.cs.st-and.ac.uk/~sal Fax +44 (1334) 463278
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