Outer automorphisms of free Burnside groups

In this paper, we study some properties of the outer automorphism group of free Burnside groups of large odd exponent. In particular, we prove that it contains free and free abelian subgroups.Comment: 19 page

Growth of periodic quotients of hyperbolic groups

Let G be a non-elementary torsion-free hyperbolic group. We prove that the exponential growth rate of the periodic quotient G/G^n tends to the one of G as n odd approaches infinity. Moreover we provide an estimate at which the convergence is taking place.Comment: 20 pages, 3 figure

Growth and order of automorphisms of free groups and free Burnside groups

We prove that an outer automorphism of the free group is exponentially growing if and only if it induces an outer automorphism of infinite order of free Burnside groups with sufficiently large odd exponent.Comment: 36 pages, 4 figure

A Cartan-Hadamard type result for relatively hyperbolic groups

In this article, we prove that if a finitely presented group has an asymptotic cone which is tree-graded with respect to a precise set of pieces then it is relatively hyperbolic. This answers a question of M. Sapir.Comment: 33 pages, 2 figure