Dear Ian,
I was trying to reproduce your computations, and, if I was following
your way correctly, then
Image(Embedding(GDirect,1),b);
will not work because b belongs to the dihedral group of order 12
which is the 2nd factor of the direct product, not the 1st one.
Thus, to embed b into the direct product, you need to use
gap> Image(Embedding(GDirect,2),b);
See my working example below:
gap> GCyclic := CyclicGroup( 2 ) ;;
gap> GDihedral := DihedralGroup( 12 ) ;;
gap> GDirect := DirectProduct(GCyclic,GDihedral);;
gap> h := GeneratorsOfGroup( GCyclic )[1] ;
f1
gap> a := GeneratorsOfGroup( GDihedral )[1] ;
f1
gap> b := GeneratorsOfGroup( GDihedral )[2] ;
f2
gap> Image(Embedding(GDirect,1),h);
f1
gap> Image(Embedding(GDirect,2),a);
f2
gap> Image(Embedding(GDirect,2),b);
f3
Hope it helps, and please do not hesitate to ask further questions.
Best wishes,
Alexander
On 16 Jan 2007, at 16:10, Ian McLoughlin wrote:
Hi,
I'm having a problem with creating a listing of the direct product
of two
groups. They are...
1) The cyclic group(C2) of order 2: < h | h^2 = 1 > and
2) The dihedral group(D12) of order 12: < a , b | a^2 = 1 , b^6
= 1 , ab
= ba^(-1) >.
What I need is a listing of the elements of C2 x D12(in a list) in
the order
that I want....
[ 1 , b , b^2 , ... , b^5 , a , ab , ab^2 , ... , ab^5 , h , hb ,
hb^2 , ...
, hb^5 , hab , hab^2 , hab^5 ].
When I try to use DirectProduct and the Image(Embedding(GDirect,1),b);
technique in other posts to this forum about direct products, I get an
error. What i tried was....
h := GeneratorsOfGroup( GCyclic )[1] ;
a := GeneratorsOfGroup( GDihedral )[1] ;
b := GeneratorsOfGroup( GDihedral )[2] ;
with
GCyclic := CyclicGroup( 2 ) ;
GDihedral := DihedralGroup( 12 ) ;
.
Thanks,
Ian
_______________________________________________
Forum mailing list
Forum@mail.gap-system.org
http://mail.gap-system.org/mailman/listinfo/forum
