It may be relevant to look at the canonical labelling used for Galois grousp (see for example http://www.lmfdb.org/GaloisGroup/ and click on the word "label").
John On 10 April 2013 14:19, Nicolas M. Thiery <nicolas.thi...@u-psud.fr> wrote: > Hi Christian, > > On Wed, Apr 10, 2013 at 07:59:49AM -0500, Christian Stump wrote: >> I wonder if there is a way to get a canonical form of a subgroup of a >> permutation group (or, even better, any group). This would be >> something like a method "canonical_labeling" for permutation groups >> that returns an isomorphic permutation group, and such that two groups >> are isomorphic if and only if their "canonical labellings" coincide. >> >> I don't think anything like that is currently implemented, right? > > Not that I know of. I would suggest to ask on the GAP mailing list if > something like this is implemented in GAP. > >> A "natural" implementation would be to compute the multiplication >> table of the group, apply the canonical form algorithm from graphs (by >> simultaneous row and column permutations of the multiplication table), >> obtain a canoncial form of the multiplication table, and turn this >> data into a canonical form of a permutation group. > > You need to act not only on rows and columns but also on the values in > the table, don't you? > > That being said, it should indeed be possible to handle this problem > by encoding the product as a ternary relation (a,b,ab), and encoding > the ternary relation itself using a graph. Something like: > > Vertices: elements a of G, and pairs (a,b) of elements of G > > Edges: a -> (a,b) with edge label "left" > b -> (a,b) with edge label "right" > (a,b) -> ab with edge label "result" > Loops: (a,b) -> (a,b) > > The loops are just here to distinguish the two kinds of vertices; one > could instead specify a vertex bipartition to the canonical labeling > function. > > Note that the above would work for any semigroup or even magma. But > one could hope for something vastly more efficient for groups. > > Cheers, > Nicolas > -- > Nicolas M. Thiéry "Isil" <nthi...@users.sf.net> > http://Nicolas.Thiery.name/ > > -- > You received this message because you are subscribed to the Google Groups > "sage-devel" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to sage-devel+unsubscr...@googlegroups.com. > To post to this group, send email to sage-devel@googlegroups.com. > Visit this group at http://groups.google.com/group/sage-devel?hl=en. > For more options, visit https://groups.google.com/groups/opt_out. > > -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-devel?hl=en. For more options, visit https://groups.google.com/groups/opt_out.
