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 <[email protected]> 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 <[email protected]> > To: krishna mohan <[email protected]> > Cc: gap forum <[email protected]> > 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: [email protected], Phone: ++1-970-4914288 > http://www.math.colostate.edu/~hulpke > > _______________________________________________ > Forum mailing list > [email protected] > http://mail.gap-system.org/mailman/listinfo/forum > -- Dmitrii Pasechnik ----- DISCLAIMER: Any text following this sentence does not constitute a part of this message, and was added automatically during transmission. CONFIDENTIALITY: This email is intended solely for the person(s) named and may be confidential and/or privileged. If you are not the intended recipient, please delete it, notify us and do not copy, use, or disclose its content. Thank you. Towards A Sustainable Earth: Print Only When Necessary _______________________________________________ Forum mailing list [email protected] http://mail.gap-system.org/mailman/listinfo/forum
