First of all, thank you so much por your invaluable help. I'm a young student and I didn't know that "the conjugacy classes of the alternating groups were well-known and there sizes could be computed easily". Anyway, I hope that this kind of computations with many conjugacy classes might be interesting in other frameworks.
I'm sorry if the ease of my question has bothered someone. Best, VMOS <div>-------- Mensaje original --------</div><div>De: Víctor Manuel Ortiz Sotomayor <vico...@doctor.upv.es> </div><div>Fecha:27/11/2016 15:44 (GMT+01:00) </div><div>Para: benjamin.samb...@gmail.com,alexander.hul...@colostate.edu </div><div>Cc: Forum@mail.gap-system.org </div><div>Asunto: [GAP Forum] Conjugacy classes Alternating group degree 125 </div><div> </div> ------------------------------------------------------------------------- > My recommendation would be to take the code for computing conjugacy > classes (which is in the file `claspcgs.gi`) and centralizers (which > works down over subsequently larger factor groups) which currently > works breadth-first to convert it to a depth-first approach, not > storing all classes, but deleting them once the size of the class is > known. > Caveat: Even the factor of Q modulo the 6th term in the lower > central series (this is less than sqrt(|Q|), so only a small bit) > already has almost 2 million conjugacy classes, so the whole group > could easily have 10^10 classes or more. which puts the feasibility > of such an enumerative approach into doubt. > Best, > Alexander Hulpke -------------------------------------------------------------------------- >> If I understand the question correctly, there is no need to use a >> computer. The conjugacy classes of the alternating groups are >> well-known and there sizes can be computed easily. But maybe this >> is not the point of the question. >> Best, >> Benjamin -------------------------------------------------------------------------- >>> Am 26.11.2016 um 16:17 schrieb Víctor Manuel Ortiz Sotomayor: >>> Let G:=AlternatingGroup(125) be the Alternating group of degree >>> 125, and let Q:=SylowSubgroup(G, 5) be a Sylow 5-subgroup of G. >>> >>> I want to compute, for each element x of Q, the distinct >>> G-conjugacy class sizes, that is, the distinct values of >>> Size(ConjugacyClass(G, x)) (obviously, computing the distinct >>> values of Centralizer(G, x) for all x in Q) would be the same). >>> >>> Needless to say that, I always get out of memory when I run over >>> all the elements of Q. I had tried the following: compute the >>> upper central series of Q (L:=UpperCentralSeriesOfGroup(Q)) and, >>> for some "intermediate" normal subgroup N in that chain, to >>> decompose Q in right cosets on N, in order to make a disjoint >>> union of the elements of Q that is more manageable. However, I >>> still have problems of memory because either I have so many >>> transversals or the order of N is also too large. Any idea? >>> >>> Thanks in advance. _______________________________________________ Forum mailing list Forum@mail.gap-system.org http://mail.gap-system.org/mailman/listinfo/forum
