Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Approximating simple locally compact groups by their dense locally
  compact subgroups   The class, denoted by $\mathscr{S}$, of totally disconnected locally compact
groups which are non-discrete, compactly generated, and topologically simple
contains many compelling examples. In recent years, a general theory for these
groups, which studies the interaction between the compact open subgroups and
the global structure, has emerged. In this article, we study the non-discrete
totally disconnected locally compact groups $H$ that admit a continuous
embedding with dense image into some $G\in \mathscr{S}$; that is, we consider
the dense locally compact subgroups of groups $G\in \mathscr{S}$. We identify a
class $\mathscr{R}$ of almost simple groups which properly contains
$\mathscr{S}$ and is moreover stable under passing to a non-discrete dense
locally compact subgroup. We show that $\mathscr{R}$ enjoys many of the same
properties previously obtained for $\mathscr{S}$ and establish various original
results for $\mathscr{R}$ that are also new for the subclass $\mathscr{S}$,
notably concerning the structure of the local Sylow subgroups and the full
automorphism group.

6
The categories of this paper are: astro-ph
30
The categories of this paper are: q-alg
37
The categories of this paper are: supr-con
5
The categories of this paper are: gr-qc
15
The categories of this paper are: nucl-ex
28
The categories of this paper are: alg-geom
21
The categories of this paper are: adap-org
4
The categories of this paper are: cond-mat
19
The categories of this paper are: eess
35
The categories of this paper are: mtrl-th
12
The categories of this paper are: nucl-th
23
The categories of this paper are: solv-int
34
The categories of this paper are: chem-ph
16
The categories of this paper are: stat
11
The categories of this paper are: hep-lat
13
The categories of this paper are: quant-ph