Topological finite generation of certain compact open subgroups of tree automorphisms.

Given a finite permutation group F on d letters, one can define a group of automorphism of a d-regular tree whose local action on the tree is given by the permutation group F. In a joint work with Marc Burger we determine when the maximal compact subgroup of this group is topologically finitely generated. This is motivated by studying uniform lattices in the group of automorphisms of a product of trees.