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Bounded automorphisms and quasi-isometries of finitely generated groups
-
Aniruddha C. Naolekar
Veröffentlicht/Copyright:
18. November 2005
Abstract
Let Γ be a finitely generated infinite group. Denote by K (Γ ) the FC-centre of Γ, i.e. the
subgroup of all elements of Γ having only finitely many conjugates in Γ. Let
QI(Γ ) denote the group of quasi-isometries of Γ with respect to a word
metric. We prove that the natural homomorphism
θΓ : Aut(Γ ) → QI(Γ ) is
a monomorphism only if K (Γ ) equals the
centre Z (Γ ) of Γ. The converse holds if
K (Γ ) = Z (Γ ) is torsion-free.
When K (Γ ) is finite we show
that 
is a monomorphism where 
= Γ| K (Γ ). We apply this criterion to a number of classes of
groups arising in combinatorial and geometric group theory.
:
Published Online: 2005-11-18
Published in Print: 2005-07-20
Walter de Gruyter GmbH & Co. KG
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Artikel in diesem Heft
- Tri-extraspecial groups
- On commutators in p-groups
- Capability of nilpotent products of cyclic groups
- Products of characters and derived length. II
- Character degree graphs, blocks and normal subgroups
- Reflection triangles in Coxeter groups and biautomaticity
- On algebraic sets over metabelian groups
- Bounded automorphisms and quasi-isometries of finitely generated groups
- Pattern recognition and minimal words in free groups of rank 2
Artikel in diesem Heft
- Tri-extraspecial groups
- On commutators in p-groups
- Capability of nilpotent products of cyclic groups
- Products of characters and derived length. II
- Character degree graphs, blocks and normal subgroups
- Reflection triangles in Coxeter groups and biautomaticity
- On algebraic sets over metabelian groups
- Bounded automorphisms and quasi-isometries of finitely generated groups
- Pattern recognition and minimal words in free groups of rank 2
