Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Characterizations of the Suzuki tower near polygons   In recent work, we constructed a new near octagon $\mathcal{G}$ from certain
involutions of the finite simple group $G_2(4)$ and showed a correspondence
between the Suzuki tower of finite simple groups, $L_3(2) < U_3(3) < J_2 <
G_2(4) < Suz$, and the tower of near polygons, $\mathrm{H}(2,1) \subset
\mathrm{H}(2)^D \subset \mathsf{HJ} \subset \mathcal{G}$. Here we characterize
each of these near polygons (except for the first one) as the unique near
polygon of the given order and diameter containing an isometrically embedded
copy of the previous near polygon of the tower. In particular, our
characterization of the Hall-Janko near octagon $\mathsf{HJ}$ is similar to an
earlier characterization due to Cohen and Tits who proved that it is the unique
regular near octagon with parameters $(2, 4; 0, 3)$, but instead of regularity
we assume existence of an isometrically embedded dual split Cayley hexagon,
$\mathrm{H}(2)^D$. We also give a complete classification of near hexagons of
order $(2, 2)$ and use it to prove the uniqueness result for $\mathrm{H}(2)^D$.

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The categories of this paper are: quant-ph
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The categories of this paper are: solv-int
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The categories of this paper are: q-alg
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The categories of this paper are: q-bio
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-th
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The categories of this paper are: physics
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The categories of this paper are: econ
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The categories of this paper are: chem-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: cond-mat
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The categories of this paper are: math-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: funct-an