Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Finite flag-transitive affine planes with a solvable automorphism group   In this paper, we consider finite flag-transitive affine planes with a
solvable automorphism group. Under a mild number-theoretic condition involving
the order and dimension of the plane, the translation complement must contain a
linear cyclic subgroup that either is transitive or has two equal-sized orbits
on the line at infinity. We develop a new approach to the study of such planes
by associating them with planar functions and permutation polynomials in the
odd order and even order case respectively. In the odd order case, we
characterize the Kantor-Suetake family by using Menichetti's classification of
generalized twisted fields and Blokhuis, Lavrauw and Ball's classifcation of
rank two commutative semifields. In the even order case, we develop a technique
to study permutation polynomials of DO type by quadratic forms and characterize
such planes that have dimensions up to four over their kernels.

5
The categories of this paper are: gr-qc
24
The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
15
The categories of this paper are: nucl-ex
18
The categories of this paper are: econ
8
The categories of this paper are: hep-ex
17
The categories of this paper are: q-fin
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The categories of this paper are: physics
9
The categories of this paper are: nlin
30
The categories of this paper are: q-alg
34
The categories of this paper are: chem-ph
35
The categories of this paper are: mtrl-th
22
The categories of this paper are: chao-dyn
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The categories of this paper are: cond-mat
29
The categories of this paper are: funct-an
37
The categories of this paper are: supr-con