Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Profinite completion and double-dual : isomorphisms and counter-examples   We define, for any group $G$, finite approximations ; with this tool, we give
a new presentation of the profinite completion $\hat{\pi} : G \to \hat{G}$ of
an abtract group $G$. We then prove the following theorem : if $k$ is a finite
prime field and if $V$ is a $k$-vector space, then, there is a natural
isomorphism between $\hat{V}$ (for the underlying additive group structure) and
the additive group of the double-dual $V^{**}$. This theorem gives
counter-examples concerning the iterated profinite completions of a group.
These phenomena don't occur in the topological case.

8
The categories of this paper are: hep-ex
25
The categories of this paper are: patt-sol
33
The categories of this paper are: plasm-ph
24
The categories of this paper are: dg-ga
22
The categories of this paper are: chao-dyn
3
The categories of this paper are: physics
14
The categories of this paper are: math-ph
6
The categories of this paper are: astro-ph
10
The categories of this paper are: q-bio
36
The categories of this paper are: cmp-lg
1
The categories of this paper are: cs
34
The categories of this paper are: chem-ph
18
The categories of this paper are: econ
30
The categories of this paper are: q-alg
21
The categories of this paper are: adap-org
26
The categories of this paper are: bayes-an