[GAP Forum] RE: Forum Digest, Vol 62, Issue 2

[Alexander Konovalov]

Dear Odilo Ndiweni,

It is not quite clear for me what namely would you like to compute,  
but of course
GAP can give you answer on a number of questions regarding subgroups  
and their
elements. Just for a short self-explaining example I create here the  
dihedral group
of order 8 as a permutation group for simplicity:

gap> D:=DihedralGroup(IsPermGroup,8);
Group([ (1,2,3,4), (2,4) ])
gap> NormalSubgroups(D);
[ Group(()), Group([ (1,3)(2,4) ]), Group([ (1,3)(2,4), (1,2)(3,4) ]),
   Group([ (1,3)(2,4), (2,4) ]), Group([ (1,2,3,4), (1,3)(2,4) ]),
   Group([ (1,2,3,4), (2,4) ]) ]
gap> MaximalSubgroups(D);
[ Group([ (2,4), (1,3)(2,4) ]), Group([ (1,2,3,4), (1,3)(2,4) ]),
   Group([ (1,2)(3,4), (1,3)(2,4) ]) ]
gap> cc:=ConjugacyClassesSubgroups(D);
[ Group( () )^G, Group( [ (1,3)(2,4) ] )^G, Group( [ (2,4) ] )^G,
   Group( [ (1,2)(3,4) ] )^G, Group( [ (1,3)(2,4), (2,4) ] )^G,
   Group( [ (1,3)(2,4), (1,2,3,4) ] )^G, Group( [ (1,3)(2,4), (1,2) 
(3,4) ] )^G,
   Group( [ (1,3)(2,4), (2,4), (1,2,3,4) ] )^G ]
gap> AsList(Representative(cc[5]));
[ (), (2,4), (1,3), (1,3)(2,4) ]

To get started, let me recommend you the following resources:

1) GAP Tutorial (a part of your GAP installation in gap4r4/doc/tut,
also online at http://www.gap-system.org/Manuals/doc/htm/tut/chapters.htm 
  ).
It has a separate chapter about Groups and Homomorphisms.

2) GAP FAQ: http://www.gap-system.org/Faq/faq.html

3) Additional materials under http://www.gap-system.org/Doc/doc.html,
in particular, in "Learning GAP" and "Teaching Material" sections.

Hope this helps!

Best,
Alexander


On 29 Jan 2009, at 09:39, Ndiweni, Odilo wrote:

> Dear all
> will love to identify elements of subgroups of dihedral groups using  
> GAP.I am still a novice in the use of the language and will be glad  
> to get all sort of ways.
>
> sincerely
>
> Odilo Ndiweni
> Mathematics Dept (Pure and Applied)
> UFH
> Phone: 040-602-2370
> Cell: 0762337318
> Email: ondiweni at ufh.ac.za