Hello all,

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?