A comment on another question (linked below) states 


"The group $PSL\_2((\mathbb{Z}/p^n))$ is the automorphisms group of the $(p+1)$ regular tree of depth $n$, where at level $m$ of the tree you have the points of $\mathbb{P}(\mathbb{Z}/p^m)$."


I was unable to find a reference stating this. Is it true, and if so what is the correct reference?


Comment: [Presentations of PSL(2, Z/p^n)](https://mathoverflow.net/questions/79197/presentations-of-psl2-z-pn/79240#79240)



$PSL_2(\mathbb{Z}/p^n)$ isomorphic to automorphism group of depth-$n$, $(p+1)$-regular tree?
As already noted in the comments, the group $G=PSL\_2(\mathbb{Z}/p^n)$ is not the full automorphism group of the $(p+1)$-regular tree of depth $n$. These particular groups of automorphisms have quite some additional structure.


For example, if one fixes any leaf $x$, then the point-stabilizer $G\_x$ contains a normal subgroup $U\_x$ which works regular on the leaves which are not in the same branch as $x$ (i.e. the leaves $y$ for which the path fro $x$ to $y$ passes the root of the tree). In this particular case, the groups $U\_x$ will be isomorphic to the additive group $\mathbb{Z}/p^n$.


