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: ondiw...@ufh.ac.za
_______________________________________________
Forum mailing list
Forum@mail.gap-system.org
http://mail.gap-system.org/mailman/listinfo/forum
