Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On transitivity and (non)amenability of Aut(F_n) actions on group
  presentations   For a finitely generated group $G$ the Nielsen graph $N_n(G)$, $n\geq
\operatorname{rank}(G)$, describes the action of the group
$\operatorname{Aut}F_n$ of automorphisms of the free group $F_n$ 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 $\operatorname{Aut}F_n$, $n\geq 4$. We prove
nonamenability of Nielsen graphs $N_n(G)$ for all $n\ge
\max\{2,\operatorname{rank}(G)\}$ when $G$ is indicable, and for $n$ big enough
when $G$ is elementary amenable. We give an explicit description of $N_d(G)$
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.

12
The categories of this paper are: nucl-th
18
The categories of this paper are: econ
8
The categories of this paper are: hep-ex
5
The categories of this paper are: gr-qc
28
The categories of this paper are: alg-geom
36
The categories of this paper are: cmp-lg
21
The categories of this paper are: adap-org
37
The categories of this paper are: supr-con
32
The categories of this paper are: atom-ph
33
The categories of this paper are: plasm-ph
16
The categories of this paper are: stat
34
The categories of this paper are: chem-ph
3
The categories of this paper are: physics
4
The categories of this paper are: cond-mat
30
The categories of this paper are: q-alg
9
The categories of this paper are: nlin