Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Translation lengths of outer automorphisms of finitely generated
  free-by-finite groups   Bestvina, Feighn and Handel proved that every subgroup of the outer
automorphism group, $\textrm{Out}(F_n)$, of the free group of rank $n$ is
either virtually finitely generated abelian or contains a nonabelian free
group. In this note we consider the more general situation of the outer
automorphism group $\textrm{Out}(G)$ of a finitely generated free-by-finite
group $G$. We show that $\textrm{Out}(G)$ is translation discrete and that
every subgroup of $\textrm{Out}(G)$ is either virtually finitely generated
abelian or contains a nonabelian free group.

1
The categories of this paper are: cs
23
The categories of this paper are: solv-int
6
The categories of this paper are: astro-ph
37
The categories of this paper are: supr-con
35
The categories of this paper are: mtrl-th
26
The categories of this paper are: bayes-an
33
The categories of this paper are: plasm-ph
34
The categories of this paper are: chem-ph
20
The categories of this paper are: acc-phys
12
The categories of this paper are: nucl-th
31
The categories of this paper are: ao-sci
21
The categories of this paper are: adap-org
29
The categories of this paper are: funct-an
4
The categories of this paper are: cond-mat
5
The categories of this paper are: gr-qc
22
The categories of this paper are: chao-dyn