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gap> TestRandom := function(n)
> local
> p,
> g,
> l,
> i;
> p := RandomPartialPerm(n);
> p := ComponentsOfPartialPerm(p);
> g := YoungGroupFromPartition(p);
> l := SubgroupLadder(g);
> for i in [2..Length(l)] do
> if Order(l[i]) < Order(l[i-1]) then
> if not (IsSubgroup(l[i-1],l[i]) and Index(l[i-1],l[i]) <= n) then
> return false;
> fi;
> else
> if not (IsSubgroup(l[i],l[i-1]) and Index(l[i],l[i-1]) <= n) then
> return false;
> fi;
> fi;
> od;
> return true;
> end;;
#
gap> TestRandom(20);
true
gap> TestRandom(30);
true
gap> TestRandom(40);
true
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