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TWISTED CONJUGACY CLASSES IN ABELIAN EXTENSIONS OF CERTAIN LINEAR GROUPS
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REIDEMEISTER SPECTRUM FOR METABELIAN GROUPS OF THE FORM Q n ⋊ Z AND Z[1/p] n ⋊ Z, p PRIME.
, 909
"... Abstract. In this note we study the Reidemeister spectrum for metabelian groups of the form Q n ⋊Z and Z[1/p] n ⋊Z. Particular attention is given to the R ∞ property of a subfamily of these groups. 1. ..."
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Abstract. In this note we study the Reidemeister spectrum for metabelian groups of the form Q n ⋊Z and Z[1/p] n ⋊Z. Particular attention is given to the R ∞ property of a subfamily of these groups. 1.
TWISTED CONJUGACY CLASSES FOR POLYFREE GROUPS
, 802
"... Abstract. Let G be a finitely generated polyfree group. If G has nonzero Euler characteristic then we show that Aut(G) has a finite index subgroup in which every automorphism has infinite Reidemeister number. When G is of length 2, we investigate which such groups have the property that for every au ..."
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Abstract. Let G be a finitely generated polyfree group. If G has nonzero Euler characteristic then we show that Aut(G) has a finite index subgroup in which every automorphism has infinite Reidemeister number. When G is of length 2, we investigate which such groups have the property that for every automorphism the number of Reidemeister classes is infinite. 1.
Twisted conjugacy classes in lattices in semisimple Lie groups. arXiv:1201.4934
, 2012
"... Abstract. Given a group automorphism φ: Γ − → Γ, one has an action of Γ on itself by φtwisted conjugacy, namely, g.x = gxφ(g−1). The orbits of this action are called φconjugacy classes. One says that Γ has the R∞property if there are infinitely many φconjugacy classes for every automorphism φ of ..."
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Abstract. Given a group automorphism φ: Γ − → Γ, one has an action of Γ on itself by φtwisted conjugacy, namely, g.x = gxφ(g−1). The orbits of this action are called φconjugacy classes. One says that Γ has the R∞property if there are infinitely many φconjugacy classes for every automorphism φ of Γ. In this paper we show that any irreducible lattice in a connected noncompact semi simple Lie group having finite centre and rank at least 2 has the R∞property. 1.
0 A RELATIONSHIP BETWEEN TWISTED CONJUGACY CLASSES AND THE GEOMETRIC INVARIANTS Ωn
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TWISTED INNER REPRESENTATIONS
"... Abstract. We study the twisted inner representations of a discrete group G on ℓ 2 (G) corresponding to the action g ↦ → xgφ(x −1) (x,g ∈ G) of G on itself, where φ is an automorphism of G. Our first results are related to amenability and the counting of Reidemeister classes (twisted conjugacy classe ..."
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Abstract. We study the twisted inner representations of a discrete group G on ℓ 2 (G) corresponding to the action g ↦ → xgφ(x −1) (x,g ∈ G) of G on itself, where φ is an automorphism of G. Our first results are related to amenability and the counting of Reidemeister classes (twisted conjugacy classes) of φ, i.e. classes x ∼ gxφ(g −1). 1.
Singleton doublytwisted conjugacy classes in free groups
, 2009
"... We give a simple method which can be used to show that an element of a free group is the only member of its doublytwisted conjugacy class with respect to a pair of homomorphisms having a natural remnant property. We also show that most pairs of homomorphisms have infinitely many such singleton clas ..."
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We give a simple method which can be used to show that an element of a free group is the only member of its doublytwisted conjugacy class with respect to a pair of homomorphisms having a natural remnant property. We also show that most pairs of homomorphisms have infinitely many such singleton classes. 1