Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Groups with the same cohomology as their profinite completions   For any positive integer $n$, $\mathcal{A}_n$ is the class of all groups $G$
such that, for $0\leq i\leq n$, $H^i(\hat{G},A)\cong H^i(G,A)$ for every finite
discrete $\hat{G}$-module $A$. We describe certain types of free products with
amalgam and HNN extensions that are in some of the classes $\mathcal{A}_n$. In
addition, we investigate the residually finite groups in the class
$\mathcal{A}_2$.

6
The categories of this paper are: astro-ph
15
The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph
1
The categories of this paper are: cs
34
The categories of this paper are: chem-ph
29
The categories of this paper are: funct-an
33
The categories of this paper are: plasm-ph
7
The categories of this paper are: hep-th
12
The categories of this paper are: nucl-th
22
The categories of this paper are: chao-dyn
36
The categories of this paper are: cmp-lg
16
The categories of this paper are: stat
37
The categories of this paper are: supr-con
23
The categories of this paper are: solv-int
13
The categories of this paper are: quant-ph
27
The categories of this paper are: comp-gas