On Mon, Mar 1, 2010 at 6:18 PM, Simon King <[email protected]> wrote: > Hi David! > > On 1 Mrz., 20:08, David Joyner <[email protected]> wrote: >> On Mon, Mar 1, 2010 at 1:26 PM, Dana Ernst <[email protected]> wrote: >> > Is there a way to obtain a subgroup lattice for finite groups? I defined >> > a finite group G and did G.? <tab> but didn't see anything that would do >> > this. Any tips? >> >> One way: >> >> sage: G = SymmetricGroup(3) >> sage: GG = gap(G) >> sage: GG.LatticeSubgroups().ConjugacyClassesSubgroups() > > OK, that's using GAP's command. But the result is not a Poset in Sage. > > I'd be interested in having a method of finite groups that returns the > subgroup lattice as, say, a directed graph (oriented edges indicating > inclusion). Then, I have a certain construction that assigns labels to > the oriented edges, so that the equivalence class of the labeled > digraph (with respect to orientation and label preserving graph > isomorphisms) is a group theoretical invariant.
Sorry, I'm not understanding exactly what you want for the vertices of the digraph. Are they subgroups or conjugacy classes of subgroups? In any case, you can specify a graph by a dictionary, so if you can first index the subgroups (or conjugacy classes of subgroups) by non-negative integers in some way, then it seems to me it should be possible to do what you want given Sage's existing graph structure. > > How much of the necessary framework is in Sage? Labeled digraphs? If > they are implemented then it should be straight forward to write the > corresponding method of finite groups, exploiting GAP's > LatticeSubgroups. Agreed. > > Best regards, > Simon > > -- > To post to this group, send email to [email protected] > To unsubscribe from this group, send email to > [email protected] > For more options, visit this group at > http://groups.google.com/group/sage-support > URL: http://www.sagemath.org > -- To post to this group, send email to [email protected] To unsubscribe from this group, send email to [email protected] For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
