Dear Forum, On Dec 19, 2012, at 9:30 AM, Frederic Vanhove <fvanh...@cage.ugent.be> wrote: > > > I have yet another question on (equivalent) group actions. > When I build an action on a set, is there way to have GAP store a bijection > between the original points on which he acts, and the labels [1..v]?
The bijection is always simple [1..v], i.e. the action is on the elements as arranged in a listi, if neccessary calling `Enumerator' on the domain. In your example this correspondence is easier to see if you explicitly take an element list for G: gap> elm:=AsSSortedList(G); [ (), (3,4), (2,3), (2,3,4), (2,4,3), (2,4), (1,2), (1,2)(3,4), (1,2,3), (1,2,3,4), (1,2,4,3), (1,2,4), (1,3,2), (1,3,4,2), (1,3), (1,3,4), (1,3)(2,4), (1,3,2,4), (1,4,3,2), (1,4,2), (1,4,3), (1,4), (1,4,2,3), (1,4)(2,3) ] gap> act:=Action(g,G,OnPoints); <permutation group with 4 generators> gap> Orbits(act); [ [ 2, 6, 7, 3, 15, 22 ], [ 4, 5, 12, 21, 20, 16, 13, 9 ], [ 8, 17, 24 ], [ 10, 14, 11, 19, 23, 18 ] ] gap> elm{ [2, 6, 7, 3, 15, 22 ]}; # one orbit [ (3,4), (2,4), (1,2), (2,3), (1,3), (1,4) ] (This is specified in the manual section 41.7 The Permutation Image of an Action http://www.gap-system.org/Manuals/doc/ref/chap41.html#X87F73CCA7921DE65 Best wishes, Alexander Hulpke -- Colorado State University, Department of Mathematics, Weber Building, 1874 Campus Delivery, Fort Collins, CO 80523-1874, USA email: hul...@math.colostate.edu, Phone: ++1-970-4914288 http://www.math.colostate.edu/~hulpke _______________________________________________ Forum mailing list Forum@mail.gap-system.org http://mail.gap-system.org/mailman/listinfo/forum