Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the residual and profinite closures of commensurated subgroups   The residual closure of a subgroup $H$ of a group $G$ is the intersection of
all virtually normal subgroups of $G$ containing $H$. We show that if $G$ is
generated by finitely many cosets of $H$ and if $H$ is commensurated, then the
residual closure of $H$ in $G$ is virtually normal. This implies that separable
commensurated subgroups of finitely generated groups are virtually normal. A
stream of applications to separable subgroups, polycyclic groups, residually
finite groups, groups acting on trees, lattices in products of trees and
just-infinite groups then flows from this main result.

31
The categories of this paper are: ao-sci
15
The categories of this paper are: nucl-ex
8
The categories of this paper are: hep-ex
11
The categories of this paper are: hep-lat
19
The categories of this paper are: eess
30
The categories of this paper are: q-alg
23
The categories of this paper are: solv-int
7
The categories of this paper are: hep-th
0
The categories of this paper are: hep-ph
20
The categories of this paper are: acc-phys
1
The categories of this paper are: cs
6
The categories of this paper are: astro-ph
33
The categories of this paper are: plasm-ph
17
The categories of this paper are: q-fin
26
The categories of this paper are: bayes-an
28
The categories of this paper are: alg-geom