[GAP Forum] complex product of two groups

[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;