Originally Posted by

**Jeze** Hello,

Thank you very much for your thoughts.

How do you couch it, for the range?

I have been trying to outline a bijection that would work, something like (F is our set) :

$\displaystyle C(\psi )^{p-1}\rightarrow F$

$\displaystyle (a_2,...,a_p) \mapsto (\psi ,a_2\circ \psi ,a_2^{-1}\circ a_3\circ \psi ,...,a_{\left \lfloor \frac{p}{2} \right \rfloor-1}^{-1}\circ a_{\left \lfloor \frac{p}{2} \right \rfloor}\circ \psi ,a_{\left \lfloor \frac{p}{2} \right \rfloor}^{-1}\circ a_{\left \lfloor \frac{p}{2} \right \rfloor+1}\circ \psi ^{-1},...,a_{p}^{-1})$

(the count must not be valid but just to give an idea)

Problem is, they have to commute...