Twisted conjugacy classes in abelian extensions of certain linear groups

Mubeena, T. ; Sankaran, Parameswaran (2012) Twisted conjugacy classes in abelian extensions of certain linear groups Canadian Mathematical Bulletin . ISSN 0008-4395

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Official URL: http://cms.math.ca/10.4153/CMB-2012-013-7

Related URL: http://dx.doi.org/10.4153/CMB-2012-013-7

Abstract

Given a group automorphism ø:Γ→Γ, one has an action of Γ on itself by ø-twisted conjugacy, namely,g.x=gxøg-1). The orbits of this action are called ø-twisted conjugacy classes. One says that has the R∞-property if there are infinitely many ø-twisted conjugacy classes for every automorphism ø of Γ. In this paper we show that SL(n,Z) and its congruence subgroups have the R∞-property. Further we show that any (countable) abelian extension of Γ has the R∞-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.

Item Type:Article
Source:Copyright of this article belongs to University of Toronto Press.
Keywords:Twisted Conjugacy Classes; Hyperbolic Groups; Lattices in Lie Groups
ID Code:96274
Deposited On:11 Dec 2012 10:53
Last Modified:11 Dec 2012 10:53

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