Roggi Möller: Independence conditions for group actions on trees

In 1970 Tits studied "property P" for group actions on trees.

He showed that if G is a group acting on a tree with property P (and satisfying some non-triviality conditions) then the subgroup generated by the stabilizers of edges is simple. In this talk I want to discuss group actions on trees that have the property that the stabilizer of every half-tree is non-trivial and apply this property to the full automorphism group of a locally finite primitive graph with more than one end. (Joint with Jan Vonk.)