As is well known, the group $PSL(2,\mathbb Z)$ is isomorphic to the free product $C\_2 \ast C\_3$ of cyclic groups of order $2$ and $3$. Call the generators of the cyclic groups $S$ and $T$.



> 
> **Problem:** Given a prime number $p$ and a natural number $n$, write a presentation of the quotient $PSL(2, \mathbb Z/p^n\mathbb Z)$ with the images of $S$ and $T$ as generators.
> 
> 
> 



Presentations of PSL(2, Z/p^n)
I usually use [Sunday's](http://dx.doi.org/10.4153/CJM-1972-118-x) presentation: see [MR0311782](https://mathscinet.ams.org/mathscinet-getitem?mr=0311782). His T has order 2 but your S will be what he denotes ST.


