Strong generating system work only for transitive group

[nborie]

My fault from #6647

The method from Gap work only for transitive group.

sage: G = PermutationGroup([[(3,4)]])
sage: G.strong_generating_system()
[[()], [()], [()], [()]]
sage: G.strong_generating_system(base_of_group=[3,1,2,4])
[[(), (3,4)], [()], [()], [()]]

If the first position is not moved by the permutation Group. Errors appears...

[nborie]

I added a patch which solve the problem...

I just changed the stabilizer method because the old version probably didn't point the right record of GAP for StabChain?. The new stabilizer method is based form the Schreier's subgroup lemma.

I ran some:

sage: G = SymmetricGroup(10)
sage: H = PermutationGroup([G.random_element() for i in range(randrange(1,3,1))])
sage: prod(map(lambda x : len(x), H.strong_generating_system()),1) == H.cardinality()
True

everytimes, it was ok... For the speed, the method strong_generating_system is pretty slow! But I have no better idea and I still misunderstand records from GAP.

[nborie]

I uploaded a new version. There was also a mistake in the doc... That's an ugly bug...