Let $T$ denote the unique (countably infinite) tree in which every vertex has degree $3$ and let $G=Aut(T)$ be the group of graph automorphisms of $T$. 


I'm interested in the properties of this group, especially in the normal subgroups of $G$. Is there a known classification of all normal subgroups? If not, what is known and what is conjectured about them?



Normal subgroups of automorphism group of infinite cubic tree
Let $G\_+$ be the index 2 subgroup of $G$, consisting of automorphisms which act on $T$ without inversions, which means that if such an automorphism preserves an edge, it fixes this edge pointwise. Equivalently, this is the subgroup of $G$ generated by (pointwise) edge-stabilizers. It follows from a paper by J.Tits in 1970 ("Sur le groupe des automorphismes d'un arbre") that the subgroup $G\_+$ is simple. Therefore, this is the only proper normal nontrivial subgroup of $G$. 


Edit. More precisely, $G\_+$ is the maximal subgroup of $G$ whose every element acts on $T$ without inversions. This subgroup necessarily has index 2 in $G$. Equivalently, if we regard $T$ as a bipartite graph, then $G\_+$ is the index 2 subgroup in $G$ preserving the parts of the vertex set. 


