Groups Acting on Trees: From Local to Global Structure

摘要

The group of automorphisms Aut T of a locally finite tree T is a locally compact211u001egroup. In this work the authors study a large class of groups of automorphisms of 211u001ea locally finite tree which exhibit a rich structure theory, analogous to that of 211u001esemisimple Lie groups. Recall that a rank one simple algebraic group G over a 211u001elocally compact non archimedean field acts on the associated Bruhat-Tits tree 211u001edelta. Thus G is a closed subgroup of Aut delta. Moreover its action on delta is 211u001elocally infinity-transitive, that is, the stabilizer of every vertex x acts 211u001etransitively on all spheres of finite radius centered at x. In this paper the 211u001eauthors study the structure of closed non-discrete subgroups of Aut T satisfying 211u001evarious local properties.