While studying some facts about generating sets for groups, I came along the the following fact, but a proof was never given, as it should be somehow trivial.
Here the fact:
Let be a finite group. Then there exists a subset so that and
When proving this, I would start like this: By Cayley's theorem is isomorphic to some permutation group . Therefore it is enough to show the claim for
Now I know that is generated by n-1 transpositions, but I dont know how to apply this on subgroups of it. Anyone can help me with the proof?