Dear Mohammad j.mamaghani, as Max Horn already pointed out most of the time you will see the alternating or the symmetric group and indeed then GAP has problems computing a stabiliser chain if you simply call Size(g) in the following situation:
gap> s := SymmetricGroup(2187); gap> x := PseudoRandom(s); gap> y := PseudoRandom(s); gap> g := Group(x,y); (this is a similar example, although not with 2187-cycles) However, you can very efficiently do gap> IsNaturalSymmetricGroup(g); true gap> IsNaturalAlternatingGroup(g); false which costs nearly no time and memory (very efficient special methods are used for these). If one of these returned true then the group knows its size without a stabiliser chain. Once both these calls return false it should be relatively safe to call gap> Size(g); since theoretical results imply that then your group is much smaller than Sym(2187) and - after all - it acts "only" on 2187 points. Then GAP should be able to compute a stabiliser chain readily. Another possibility is to use the recog package, which does this analysis automatically in its RecogniseGroup function. Note however that this package currently only provides Monte Carlo algorithms which might go wrong. Cheers, Max On Mon, Aug 16, 2010 at 08:19:32AM -0700, mohammad j.mamaghani wrote: > I would like to calculate the order of a subgroup of symmetric group S_2187 > generated by two cycles of length 2187=3^7 using GAP, but gap has not enough > space and does not accept all the members of the cycles . Are there any ways > to use GAP for this problem?best regards mamaghaniAllameh Tabatabaei > university dept of maths and statsTehran, Iran. > > > > _______________________________________________ > Forum mailing list > Forum@mail.gap-system.org > http://mail.gap-system.org/mailman/listinfo/forum -- Max Neunhoeffer http://www-groups.mcs.st-and.ac.uk/~neunhoef/ > > > > > > > > > > > May the Source be with you! < < < < < < < < < < < < The University of St Andrews is a registered Scottish charity: No SC013532 _______________________________________________ Forum mailing list Forum@mail.gap-system.org http://mail.gap-system.org/mailman/listinfo/forum
