Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Coset-wise affine functions and cycle types of complete mappings   Let $K$ be a finite field of characteristic $p$. We study a certain class of
functions $K\rightarrow K$ that agree with an $\mathbb{F}_p$-affine function
$K\rightarrow K$ on each coset of a given additive subgroup $W$ of $K$ - we
call them $W$-coset-wise $\mathbb{F}_p$-affine functions of $K$. We show that
these functions form a permutation group on $K$ with the structure of an
imprimitive wreath product and characterize which of them are complete mappings
of $K$. As a consequence, we are able to provide various new examples of cycle
types of complete mappings of $K$, including that $K$ has a complete mapping
moving all elements of $K$ in one cycle if $p>2$.

35
The categories of this paper are: mtrl-th
27
The categories of this paper are: comp-gas
30
The categories of this paper are: q-alg
12
The categories of this paper are: nucl-th
7
The categories of this paper are: hep-th
4
The categories of this paper are: cond-mat
28
The categories of this paper are: alg-geom
13
The categories of this paper are: quant-ph
33
The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph
22
The categories of this paper are: chao-dyn
21
The categories of this paper are: adap-org
16
The categories of this paper are: stat
25
The categories of this paper are: patt-sol
36
The categories of this paper are: cmp-lg
37
The categories of this paper are: supr-con