Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Finite simple groups and localization   The purpose of this paper is to explore the concept of localization, which
comes from homotopy theory, in the context of finite simple groups. We give an
easy criterion for a finite simple group to be a localization of some simple
subgroup and we apply it in various cases. Iterating this process allows us to
connect many simple groups by a sequence of localizations. We prove that all
sporadic simple groups (except possibly the Monster) and several groups of Lie
type are connected to alternating groups. The question remains open whether or
not there are several connected components within the family of finite simple
groups.

7
The categories of this paper are: hep-th
33
The categories of this paper are: plasm-ph
12
The categories of this paper are: nucl-th
25
The categories of this paper are: patt-sol
10
The categories of this paper are: q-bio
22
The categories of this paper are: chao-dyn
0
The categories of this paper are: hep-ph
8
The categories of this paper are: hep-ex
4
The categories of this paper are: cond-mat
34
The categories of this paper are: chem-ph
18
The categories of this paper are: econ
31
The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys
21
The categories of this paper are: adap-org
11
The categories of this paper are: hep-lat
15
The categories of this paper are: nucl-ex