Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A note on torsion subgroups of groups acting on finite-dimensional
  CAT(0) cube complexes   In this article, we state and prove a general criterion which prevents some
groups from acting properly on finite-dimensional CAT(0) cube complexes. As an
application, we show that, for every non-trivial finite group $F$, the
lamplighter group $F \wr \mathbb{F}_2$ over a free group does not act properly
on a finite-dimensional CAT(0) cube complex (although it acts properly on a
infinite-dimensional CAT(0) cube complex). We also deduce from this general
criterion that, roughly speaking, given a group $G$ acting on a CAT(0) cube
complex of finite dimension and an infinite torsion subgroup $L \leq G$, either
the normaliser $N_G(L)$ is close to be free abelian or, for every $k \geq 1$,
$N_G(L)$ contains a non-abelian free subgroup commuting with a subgroup of $L$
of size $\geq k$.

7
The categories of this paper are: hep-th
35
The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc
24
The categories of this paper are: dg-ga
29
The categories of this paper are: funct-an
33
The categories of this paper are: plasm-ph
32
The categories of this paper are: atom-ph
12
The categories of this paper are: nucl-th
21
The categories of this paper are: adap-org
34
The categories of this paper are: chem-ph
4
The categories of this paper are: cond-mat
17
The categories of this paper are: q-fin
1
The categories of this paper are: cs
13
The categories of this paper are: quant-ph
22
The categories of this paper are: chao-dyn
6
The categories of this paper are: astro-ph