Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Reduced fusion systems over $p$-groups with abelian subgroup of index
  $p$: III   We finish the classification, begun in two earlier papers, of all simple
fusion systems over finite nonabelian $p$-groups with an abelian subgroup of
index $p$. In particular, this gives many new examples illustrating the
enormous variety of exotic examples that can arise. In addition, we classify
all simple fusion systems over infinite nonabelian discrete $p$-toral groups
with an abelian subgroup of index $p$. In all of these cases (finite or
infinite), we reduce the problem to one of listing all $\mathbb{F}_pG$-modules
(for $G$ finite) satisfying certain conditions: a problem which was solved in
the earlier paper by Craven, Oliver, and Semeraro using the classification of
finite simple groups.

18
The categories of this paper are: econ
9
The categories of this paper are: nlin
8
The categories of this paper are: hep-ex
23
The categories of this paper are: solv-int
16
The categories of this paper are: stat
32
The categories of this paper are: atom-ph
13
The categories of this paper are: quant-ph
4
The categories of this paper are: cond-mat
24
The categories of this paper are: dg-ga
19
The categories of this paper are: eess
5
The categories of this paper are: gr-qc
12
The categories of this paper are: nucl-th
27
The categories of this paper are: comp-gas
7
The categories of this paper are: hep-th
3
The categories of this paper are: physics
14
The categories of this paper are: math-ph