Abstract:
Let G be a group and let Ø : Γ → Γ be an endomorphism. We define an action
g.x := gxØ(g-1), for g,x ε Γ, of Γ on itself. The Ø-twisted conjugacy
class of an element x ε Γ is the orbit of this action containing x. A group
Γ has the R∞ -property if every automorphism Ø of Γ has infinitely many
Ø-twisted conjugacy classes. In this thesis it is shown that any irreducible
lattice in a non-compact connected semisimple Lie group with finite center
and having real rank at least 2 has the R∞ -property. It is also shown that
any countable abelian extensions Λ of Γ has the R∞-property when (i) the
lattice Γ is linear, (ii) Γ is a torsion free non-elementary hyperbolic group.
Also considered, the R∞-problem for S -arithmetic lattices.
