Geodesic
Commensurators and classifying spaces with virtually cyclic stabilizers
Dieter Degrijse1 ; Nansen Petrosyan2
1University of Copenhagen, Denmark
2University of Southampton, UK
Groups, geometry, and dynamics, Tome 7 (2013) no. 3, pp. 543-555

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DOI

By examining commensurators of virtually cyclic groups, we show that for each natural number n, any locally finite-by-virtually cyclic group of cardinality אn​ admits a finite dimensional classifying space with virtually cyclic stabilizers of dimension n+3. As a corollary, we prove that every elementary amenable group of finite Hirsch length and cardinality אn​ admits a finite dimensional classifying space with virtually cyclic stabilizers.
DOI : 10.4171/ggd/196
Classification : 55-XX, 20-XX
Mots-clés : Commensurator, classifying space, elementary amenable group

Dieter Degrijse  1   ; Nansen Petrosyan  2

1 University of Copenhagen, Denmark
2 University of Southampton, UK 
Dieter Degrijse; Nansen Petrosyan. Commensurators and classifying spaces  with virtually cyclic stabilizers. Groups, geometry, and dynamics, Tome 7 (2013) no. 3, pp. 543-555. doi: 10.4171/ggd/196
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     title = {Commensurators and classifying spaces  with virtually cyclic stabilizers},
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     pages = {543--555},
     year = {2013},
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     number = {3},
     doi = {10.4171/ggd/196},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/196/}
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