Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Rough ends of infinite primitive groups   If $G$ is a group of permutations of a set $\Omega$, then the suborbits of
$G$ are the orbits of point-stabilisers $G_\alpha$ acting on $\Omega$. The
cardinalities of these suborbits are the subdegrees of $G$. Every infinite
primitive permutation group $G$ with finite subdegrees acts faithfully as a
group of automorphisms of a locally-finite connected vertex-primitive directed
graph $\Gamma$ with vertex set $\Omega$, and there is consequently a natural
action of $G$ on the ends of $\Gamma$.
  We show that if $G$ is closed in the permutation topology of pointwise
convergence, then the structure of $G$ is determined by the length of any orbit
of $G$ acting on the ends of $\Gamma$.
  Examining the ends of a Cayley graph of a finitely generated group to
determine the structure of the group is often fruitful. B. Kr{\"o}n and R. G.
M{\"o}ller have recently generalised the Cayley graph to what they call a {\it
rough Cayley graph}, and they call the ends of this graph the {\it rough ends}
of the group.
  It transpires that the ends of $\Gamma$ are the rough ends of $G$, and so our
result is equivalent to saying that the structure of a closed primitive group
$G$ whose subdegrees are all finite is determined by the length of any orbit of
$G$ on its rough ends.

29
The categories of this paper are: funct-an
28
The categories of this paper are: alg-geom
14
The categories of this paper are: math-ph
35
The categories of this paper are: mtrl-th
13
The categories of this paper are: quant-ph
25
The categories of this paper are: patt-sol
11
The categories of this paper are: hep-lat
6
The categories of this paper are: astro-ph
27
The categories of this paper are: comp-gas
17
The categories of this paper are: q-fin
12
The categories of this paper are: nucl-th
37
The categories of this paper are: supr-con
30
The categories of this paper are: q-alg
36
The categories of this paper are: cmp-lg
32
The categories of this paper are: atom-ph
10
The categories of this paper are: q-bio