[GAP Forum] subgroup lattices

[John McDermott]

Dear William,

the Forum mailing list software strips attachments so yours have not appeared here. You could send them directly to Sumeyra, of course.

Best wishes,
John

On 7 Dec 2011, at 22:02, William DeMeo wrote:

> 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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--
John McDermott
Scientific Officer
Centre for Interdisciplinary Research in Computational Algebra
School of Computer Science
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