On 2012-03-08, at 06:07 , Vipul Naik wrote:
> There are two problems with your code.
>
> The first is that LatticeSubgroups is not the set of subgroups but a
> different kind of structure. If you want to access all the subgroups,
> you should use the function Subgroups. This requires the SONATA
> package or some other equivalent package -- you can load that using
> LoadPackage("sonata");.
A simpler solution (avoiding the use of Sonata) would be to use
Flat (List (ConjugacyClassesSubgroups (G), Elements))
to compute a list of subgroups of the group G.
> The problem is that GAP doesn't understand "HK" to be the product of H
> and K but rather thinks that that is a new variable.
Computing and comparing the sets H*K and K*H works for small groups, but in
general, it is much more efficient to check if
| <H, K> | • | H cap K | = |H| |K|,
or, in GAP code,
PermutingSubgroups := function(H,K)
return Size (ClosureGroup (H, K)) * Size (Intersection (H, K)) =
Size(H)*Size(K);
end;
Cheers
Burkhard.
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