Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Group cohomology and control of p-fusion   We show that if an inclusion of finite groups H < G of index prime to p
induces a homeomorphism of mod p cohomology varieties, or equivalently an
F-isomorphism in mod p cohomology, then H controls p-fusion in G, if p is odd.
This generalizes classical results of Quillen who proved this when H is a Sylow
p-subgroup, and furthermore implies a hitherto difficult result of Mislin about
cohomology isomorphisms. For p=2 we give analogous results, at the cost of
replacing mod p cohomology with higher chromatic cohomology theories.
  The results are consequences of a general algebraic theorem we prove, that
says that isomorphisms between p-fusion systems over the same finite p-group
are detected on elementary abelian p-groups if p odd and abelian 2-groups of
exponent at most 4 if p=2.

15
The categories of this paper are: nucl-ex
0
The categories of this paper are: hep-ph
33
The categories of this paper are: plasm-ph
32
The categories of this paper are: atom-ph
14
The categories of this paper are: math-ph
8
The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg
24
The categories of this paper are: dg-ga
16
The categories of this paper are: stat
10
The categories of this paper are: q-bio
37
The categories of this paper are: supr-con
13
The categories of this paper are: quant-ph
1
The categories of this paper are: cs
36
The categories of this paper are: cmp-lg
20
The categories of this paper are: acc-phys
4
The categories of this paper are: cond-mat