Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Subgroups of finite index and the just infinite property   A residually finite (profinite) group $G$ is just infinite if every
non-trivial (closed) normal subgroup of $G$ is of finite index. This paper
considers the problem of determining whether a (closed) subgroup $H$ of a just
infinite group is itself just infinite. If $G$ is not virtually abelian, we
give a description of the just infinite property for normal subgroups in terms
of maximal subgroups. In particular, we show that such a group $G$ is
hereditarily just infinite if and only if all maximal subgroups of finite index
are just infinite. We also obtain results for certain families of virtually
abelian groups, including all virtually abelian pro-$p$ groups and their
discrete analogues.

5
The categories of this paper are: gr-qc
19
The categories of this paper are: eess
13
The categories of this paper are: quant-ph
21
The categories of this paper are: adap-org
28
The categories of this paper are: alg-geom
14
The categories of this paper are: math-ph
29
The categories of this paper are: funct-an
10
The categories of this paper are: q-bio
23
The categories of this paper are: solv-int
9
The categories of this paper are: nlin
34
The categories of this paper are: chem-ph
15
The categories of this paper are: nucl-ex
37
The categories of this paper are: supr-con
17
The categories of this paper are: q-fin
35
The categories of this paper are: mtrl-th
27
The categories of this paper are: comp-gas