[GAP Forum] complex product of two groups

[William DeMeo]

Thanks for the suggestion, but the direct product is not my friend in this
case.  (In particular, the direct product is a group.  HK is not always a
group.)
On Apr 18, 2012 3:11 AM, "Ivo Hedtke" <hedtke at me.com> wrote:

> 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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>
>