Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Study of Groups through Transversals   In this note, a necessary and sufficient condition for the normalizer of a
core-free subgroup $H$ of a finite group $G$ to be normal in $G$ is obtained.
Also, a known result of finite groups is obtained through transversal.

14
The categories of this paper are: math-ph
7
The categories of this paper are: hep-th
17
The categories of this paper are: q-fin
5
The categories of this paper are: gr-qc
23
The categories of this paper are: solv-int
20
The categories of this paper are: acc-phys
22
The categories of this paper are: chao-dyn
26
The categories of this paper are: bayes-an
36
The categories of this paper are: cmp-lg
31
The categories of this paper are: ao-sci
4
The categories of this paper are: cond-mat
15
The categories of this paper are: nucl-ex
3
The categories of this paper are: physics
30
The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph
35
The categories of this paper are: mtrl-th