Helloooooo everybody !!! I am but a humble graph theoretician, and I recently ended up playing with the automorphism groups of my dear objects in order to find good ways to plot them. This I do directly with GAP when I do not use it through Sage, but I currently have a very technical problem and I would be delighted if you happened to have already implemented somewhere the feature I am looking for :-)
Here it is : I have a permutation group G, or a group acting on a set of vertices in a graph, which sometime turns out to be imprimitive [1], which means (I learned that recently) that there exists a nontrivial partition P = P1, ... P_k of my set of vertices such that the image of any P_i by an element of G is another element of P. I do not know yet whether GAP can tell me whether a given permutation group is primitive, but more than that I would be interested in obtaining -- when it is not the case -- an example of partition which is preserved in such a way. Actually, because I am *very* greedy, I would ideally like to obtain an inclusionwise "finest" (or smallest) partition, and in an ideal world to enumerate them all. May it be a task that GAP can solve ? :-) Thank you very much for your help ! Nathann [1] http://en.wikipedia.org/wiki/Primitive_permutation_group _______________________________________________ Forum mailing list Forum@mail.gap-system.org http://mail.gap-system.org/mailman/listinfo/forum
