Dimension and randomness in groups acting on rooted trees

Dimension and Randomness in Groups Acting on Rooted Trees

Dimension and Randomness in Groups Acting on Rooted Trees

Dimension and randomness in groups acting on rooted trees by Miklós Abért ∗ and

We explore the structure of the p-adic automorphism group Γ of the infinite rooted regular tree. We determine the asymptotic order of a typical element, answering an old question of Turán. We initiate the study of a general dimension theory of groups acting on rooted trees. We describe the relationship between dimension and other properties of groups such as solvability, existence of dense free...

ON QUASI UNIVERSAL COVERS FOR GROUPS ACTING ON TREES WITH INVERSIONS

Abstract. In this paper we show that if G is a group acting on a tree X with inversions and if (T Y ) is a fundamental domain for the action of G on X, then there exist a group &tildeG and a tree &tildeX induced by (T Y ) such that &tildeG acts on &tildeX with inversions, G is isomorphic to &tilde G, and X is isomorphic to &tildeX. The pair (&tilde G &tildeX) is called the quasi universal cover...

Free subgroups in groups acting on rooted trees

We show that if a group G acting faithfully on a rooted tree T has a free subgroup, then either there exists a point w of the boundary @T and a free subgroup of G with trivial stabilizer ofw, or there existsw 2 @T and a free subgroup ofG fixingw and acting faithfully on arbitrarily small neighborhoods of w. This can be used to prove the absence of free subgroups for different known classes of g...