[GAP Forum] complex product of two groups

[Ivo Hedtke]

Hi William,

I think "DirectProduct" is your friend:

gap> H:=Group((1,2,3));
Group([ (1,2,3) ])
gap> K:=Group((1,2,4));
Group([ (1,2,4) ])
gap> DirectProduct(H,K);
Group([ (1,2,3), (4,5,6) ])

Ivo.

Am 18.04.2012 um 14:49 schrieb William DeMeo:

> Dear Forum,
> 
> If I have two subgroups H and K of a group G, what's the best way to
> form what I think is sometimes called the "complex product"?  That is,
> I want to form the set
> 
> HK = { hk : h in H, k in K }
> 
> (I don't want the group generated by H and K.)
> 
> Below is a listing of the obvious/dumb algorithm, but I suspect
> there's a better way to do this in GAP.  If someone knows of one,
> please let me know.
> 
> Thanks!
> -William
> 
> 
> HK:=[];
> for h in H do
>   for k in K do
>      if h*k not in HK then
>         Add(HK,h*k);
>      fi;
>   od;
> od;
> 
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