Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Extended F_4-buildings and the Baby Monster   The Baby Monster group B acts naturally on a geometry E(B) with diagram
c.F_4(t) for t=4 and the action of B on E(B) is flag-transitive. It possesses
the following properties:
  (a) any two elements of type 1 are incident to at most one common element of
type 2, and
  (b) three elements of type 1 are pairwise incident to common elements of type
2 iff they are incident to a common element of type 5.
  It is shown that E(B) is the only (non-necessary flag-transitive)
c.F_4(t)-geometry, satisfying t=4, (a) and (b), thus obtaining the first
characterization of B in terms of an incidence geometry, similar in vein to one
known for classical groups acting on buildings. Further, it is shown that E(B)
contains subgeometries E(^2E_6(2)) and E(Fi22) with diagrams c.F_4(2) and
c.F_4(1). The stabilizers of these subgeometries induce on them flag-transitive
actions of ^2E_6(2):2 and Fi22:2, respectively. Three further examples for t=2
with flag-transitive automorphism groups are constructed. A complete list of
possibilities for the isomorphism type of the subgraph induced by the common
neighbours of a pair of vertices at distance 2 in an arbitrary c.F_4(t)
satisfying (a) and (b) is obtained.

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The categories of this paper are: chem-ph
13
The categories of this paper are: quant-ph
0
The categories of this paper are: hep-ph
28
The categories of this paper are: alg-geom
1
The categories of this paper are: cs
11
The categories of this paper are: hep-lat
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The categories of this paper are: plasm-ph
18
The categories of this paper are: econ
3
The categories of this paper are: physics
12
The categories of this paper are: nucl-th
10
The categories of this paper are: q-bio
35
The categories of this paper are: mtrl-th
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The categories of this paper are: dg-ga
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The categories of this paper are: patt-sol
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The categories of this paper are: supr-con
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The categories of this paper are: bayes-an