[GAP Forum] Direct Product

[Ian McLoughlin]

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


--
Ian McLoughlin
emailme at ianmcloughlin.com