[GAP Forum] Using xgap to display only conjugacy classes

[Russ Woodroofe]

Dear Vincent, all,
The ordering of conjugacy classes can be kind of complicated.  But if you're in a nice enough group (or are willing to compromise a bit on what lines are shown) then you can try the following:

gap> G:=AlternatingGroup(5);
gap> GraphicSubgroupLattice(G);
  then go back to the command line and type
gap> List(ConjugacyClassesSubgroups(G), x->Representative(x));
  then go back to the graphic sheet and choose Subgroups | Insert Vertices from GAP

This code will choose a representative for each conjugacy class, and order them by inclusion.  As I allude above, that might not be the ordering you're looking for.

You could also write a routine to display the conjugacy classes with a more canonical ordering (say, the one where A^G < B^G if any element of the conjugacy class of A is contained in any element of the class of B), but it would take some bit of coding.  I could talk you through getting started if you wanted to do that.

In my own research, frequently I want to look at all subgroups, but only at a certain part of the subgroup lattice.  Similar interaction to what I've shown between GAP commands and Insert Vertices from GAP (plus its counterpart SelectedGroups to GAP) can be very helpful for this.

If you're looking at a large subgroup lattice, I'll also remark that Poset | Magnify Lattice and Poset | Resize Lattice are helpful.
Best,

  --Russ

> On 3 Sep 2019, at 23:35, Vincent Giambalvo <vince37 at hawaii.edu> wrote:
> 
> The GraphicSubroutineLattice seems not to want to graph only conjugacy classes, the menus say all subgroups. Have I overcooked something simple, or can the routine be adapted. There are simply too many subgroups. 
> Thanks for your help.
> 
> Sent from my iPad
> 
>> On Aug 14, 2019, at 3:06 AM, David Madore <david+gapforum at madore.org> wrote:
>> 
>>> On Wed, Aug 14, 2019 at 10:18:19AM +0200, Thomas Breuer wrote:
>>> For the moment, reading the GAP code appended below into a GAP session
>>> yields the desired functionality.
>> 
>> Thanks a lot for this code!  I can confirm that this worked as
>> intended.
>> s
>> -- 
>>    David A. Madore
>>  ( http://www.madore.org/~david/ )
>> 
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