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Twisted Conjugacy Classes in Abelian Extensions of Certain Linear Groups
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AbstractGiven a group automorphismϕ: Γ → Γ, one has an action of Γ on itself byϕ-twisted conjugacy, namely,g.x = gxϕ(g-1). The orbits of this action are calledϕ-twisted conjugacy classes. One says that Γ has theR∞-property if there are infinitely manyϕ-twisted conjugacy classes for every automorphismϕof Γ. In this paper we show that SL(n; Z) and its congruence subgroups have the R8-property. Further we show that any (countable) abelian extension of Γ has the R8-property where Γ is a torsion free non-elementary hyperbolic group, or SL(n; Z); Sp(2n; Z) or a principal congruence subgroup of SL(n; Z) or the fundamental group of a complete Riemannian manifold of constant negative curvature.
Title: Twisted Conjugacy Classes in Abelian Extensions of Certain Linear Groups
Description:
AbstractGiven a group automorphismϕ: Γ → Γ, one has an action of Γ on itself byϕ-twisted conjugacy, namely,g.
x = gxϕ(g-1).
The orbits of this action are calledϕ-twisted conjugacy classes.
One says that Γ has theR∞-property if there are infinitely manyϕ-twisted conjugacy classes for every automorphismϕof Γ.
In this paper we show that SL(n; Z) and its congruence subgroups have the R8-property.
Further we show that any (countable) abelian extension of Γ has the R8-property where Γ is a torsion free non-elementary hyperbolic group, or SL(n; Z); Sp(2n; Z) or a principal congruence subgroup of SL(n; Z) or the fundamental group of a complete Riemannian manifold of constant negative curvature.
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