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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