Geodesic
On transitivity and (non)amenability of Aut $F_n$ actions on group presentations
Aglaia Myropolska1 ; Tatiana Nagnibeda1 orcid
1Université de Genève, Switzerland
Groups, geometry, and dynamics, Tome 8 (2014) no. 3, pp. 837-861

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DOI

For a finitely generated group G the Nielsen graph Nn​(G), n≥rank(G), describes the action of the group AutFn​ of automorphisms of the free group Fn​ on generating n-tuples of G by elementary Nielsen moves. The question of (non)amenability of Nielsen graphs is of particular interest in relation with the open question about Property (T) for AutFn​, n≥4. We prove nonamenability of Nielsen graphs Nn​(G) for all n≥max{2,rank(G)} when G is indicable, and for n big enough when G is elementary amenable. We give an explicit description of Nd​(G) for relatively free (in some variety) groups of rank d and discuss their connectedness and nonamenability. Examples considered include free polynilpotent groups and free Burnside groups.
DOI : 10.4171/ggd/250
Classification : 00-XX
Mots-clés : Automorphisms group of a free group, generating set, transitive action, amenable graph

Aglaia Myropolska  1   ; Tatiana Nagnibeda  1

1 Université de Genève, Switzerland 
Aglaia Myropolska; Tatiana Nagnibeda. On transitivity and (non)amenability of Aut $F_n$ actions on group presentations. Groups, geometry, and dynamics, Tome 8 (2014) no. 3, pp. 837-861. doi: 10.4171/ggd/250
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     title = {On transitivity and (non)amenability of {Aut} $F_n$ actions on group presentations},
     journal = {Groups, geometry, and dynamics},
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