> 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;
To avoid checking for duplicates, you could use
HK := [];
for h in H do
for k in RightTransversal (K, Intersection (H, K)) do
Add (HK, h*k);
od;
od;
But do you really want HK as a list? You might be better off representing it as
a list of riight cosets of H (or left cosets of K).
Cheers
Burkhard.
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