[GAP Forum] Forming only groups smaller than a certain size

[Asst. Prof. Dmitrii (Dima) Pasechnik]

Dear Krishna,
you might try computing the orbit of a random vector (or few random
vectors) under your group G.
This is faster than computing the group order, and the length
of the orbit is a lower bound on |G|.
(and it is easy to tweak the orbit computation code to make it stop after
it generates more than prescribed number of elements of the orbit)

HTH,
Dmitrii


On 19 July 2010 07:55, krishna mohan <trebauchet1986 at yahoo.co.in> wrote:
> Hi..
>
>    I am using matrices as generators. The set of generators consist of just 2
> elements. Each element by itself generates a small group.
>
>
> Krishnamohan
>
>
>
>
>
> ________________________________
> From: Alexander Hulpke <ahulpke at gmail.com>
> To: krishna mohan <trebauchet1986 at yahoo.co.in>
> Cc: gap forum <forum at gap-system.org>
> Sent: Mon, 19 July, 2010 4:33:54 AM
> Subject: Re: [GAP Forum] Forming only groups smaller than a certain size
>
> Dear Forum,
>
> Krishna Mohan asked:
>
>> Currently I am running a code which generates groups from a set of generators,
>
>> which in turn depends on an integer n running in the loop.  Now the problem is
>
>> that some groups that are generated have very large sizes (of the order of
>> thousands). But I am only interested in groups that have a size less than, say,
>>
>> thousand.
>>
>> I am using the command GroupWithGenerators to generate the groups.
>>
>> Is there some way I can tell GAP to stop forming the group as soon as it finds
>
>> out that the order is greater than thousand. This will cut down the running
>>time
>>
>> of the code considerably.
>
> This really depends substantially what your generators are (permutations?
> matrices?), of what degree etc. and how many generators you have.
>
> In general, forming the group takes no time, but the initial order calculation
> (which sets up some data structures) does. There is no way provided that would
> kill this calculation once the order gets bigger -- instead one should do some
> cheap tests first that will eliminate the ``bad'' cases. What tests to do again
> depends on the elements you have, for examples:
> - try a subset of generators first
> - in the case of permutation groups, test whether the group is symmetric or
> alternating.
>
> Please feel free to provide further details of what elements and generating sets
> you are working with and I can probably be more specific.
>
> Best,
>
>    Alexander Hulpke
>
>
>
> -- Colorado State University, Department of Mathematics,
> Weber Building, 1874 Campus Delivery, Fort Collins, CO 80523-1874, USA
> email: hulpke at math.colostate.edu, Phone: ++1-970-4914288
> http://www.math.colostate.edu/~hulpke
>
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>



--
Dmitrii Pasechnik
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