Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the group of a rational maximal bifix code   We give necessary and sufficient conditions for the group of a rational
maximal bifix code $Z$ to be isomorphic with the $F$-group of $Z\cap F$, when
$F$ is recurrent and $Z\cap F$ is rational. The case where $F$ is uniformly
recurrent, which is known to imply the finiteness of $Z\cap F$, receives
special attention.
  The proofs are done by exploring the connections with the structure of the
free profinite monoid over the alphabet of $F$.

5
The categories of this paper are: gr-qc
36
The categories of this paper are: cmp-lg
30
The categories of this paper are: q-alg
17
The categories of this paper are: q-fin
15
The categories of this paper are: nucl-ex
20
The categories of this paper are: acc-phys
22
The categories of this paper are: chao-dyn
34
The categories of this paper are: chem-ph
6
The categories of this paper are: astro-ph
3
The categories of this paper are: physics
29
The categories of this paper are: funct-an
10
The categories of this paper are: q-bio
7
The categories of this paper are: hep-th
23
The categories of this paper are: solv-int
28
The categories of this paper are: alg-geom
16
The categories of this paper are: stat