[GAP Forum] subgroup lattices

[William DeMeo]

Dear Sumeyra,

Could you be more specific?

1. What GAP commands did you try?

2. What do you mean by "I want the subgroup lattice of..."

Do you want a picture of it?  Do you want a list of ALL the subgroups?
 Usually that's not as helpful as the list of conjugacy classes of
subgroups that GAP provides.  When I run the following GAP commands on
your group, they seem to work well:

gap> g:=SmallGroup(32,26);
gap> l:=LatticeSubgroups(g);
gap> ConjugacyClassesSubgroups(l);
gap> MaximalSubgroupsLattice(l);

The output of MaximalSubgroupsLattice is a little bit hard to
interpret at first, but you get used to it.  If you want a list of all
the subgroups and their covering relations, you could do the
following, at least for small groups:

gap> e:=Group([Identity(g)]);;
gap> IntermediateSubgroups(g,e);

If you want to see a picture of the subgroup lattice, you might try
XGAP.  Alternatively, you could try the universal algebra calculator
(www.uacalc.org) along with my GAP script, gap2uacalc.g (attached),
which converts a GAP group or transitive G-set into an algebra file
that can be read by uacalc.  You can then use uacalc to analyze the
structure of the subgroup lattice or the lattice of congruence
relations, and you can generate rotating 3d diagrams.  A picture of
such a diagram for your group is attached.

Hope that helps!

-William



On Wed, Dec 7, 2011 at 11:38 AM, sumeyra uskudar <suskudar at gmail.com> wrote:
> I have a problem with the command "SetPrintLevel".
> I want for example the subgrouplattice of the smallgroup (32,26) ,but it
> does not give the entirelist of subgroups with representatives.
> I think it has something to do with printlevel. but I could not set it
> altough I followed the instructions in manual.
> Anyone can help me?
>
> --
> *Sümeyra Bedir*
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