Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Isotopic classes of Transversals   Let $G$ be a finite group and $H$ be a subgroup of $G$. In this paper, we
prove that if $G$ is a finite nilpotent group and $H$ a subgroup of $G$, then
$H$ is normal in $G$ if and only if all normalized right transversals of $H$ in
$G$ are isotopic, where the isotopism classes are formed with respect to
induced right loop structures. We have also determined the number isotopy
classes of transversals of a subgroup of order 2 in $D_{2p}$, the dihedral
group of order $2p$, where $p$ is an odd prime.

16
The categories of this paper are: stat
12
The categories of this paper are: nucl-th
30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
14
The categories of this paper are: math-ph
7
The categories of this paper are: hep-th
6
The categories of this paper are: astro-ph
1
The categories of this paper are: cs
20
The categories of this paper are: acc-phys
23
The categories of this paper are: solv-int
22
The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio
5
The categories of this paper are: gr-qc
13
The categories of this paper are: quant-ph
31
The categories of this paper are: ao-sci
15
The categories of this paper are: nucl-ex