Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Some subgroups of a finite field and their applications for obtaining
  explicit factors   Let $\mathcal{S}_q$ denote the group of all square elements in the
multiplicative group $\mathbb{F}_q^*$ of a finite field $\mathbb{F}_q$ of odd
characteristic containing $q$ elements. Let $\mathcal{O}_q$ be the set of all
odd order elements of $\mathbb{F}_q^*$. Then $\mathcal{O}_q$ turns up as a
subgroup of $\mathcal{S}_q$. In this paper, we show that
$\mathcal{O}_q=\langle4\rangle$ if $q=2t+1$ and, $\mathcal{O}_q=\langle
t\rangle $ if $q=4t+1$, where $q$ and $t$ are odd primes. This paper also gives
a direct method for obtaining the coefficients of irreducible factors of
$x^{2^nt}-1$ in $\mathbb{F}_q[x]$ using the information of generator elements
of $\mathcal{S}_q$ and $\mathcal{O}_q$, when $q$ and $t$ are odd primes such
that $q=2t+1$ or $q=4t+1$.

32
The categories of this paper are: atom-ph
22
The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc
37
The categories of this paper are: supr-con
6
The categories of this paper are: astro-ph
17
The categories of this paper are: q-fin
12
The categories of this paper are: nucl-th
34
The categories of this paper are: chem-ph
25
The categories of this paper are: patt-sol
13
The categories of this paper are: quant-ph
33
The categories of this paper are: plasm-ph
15
The categories of this paper are: nucl-ex
11
The categories of this paper are: hep-lat
21
The categories of this paper are: adap-org
28
The categories of this paper are: alg-geom