Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: More on the Non-Solvable Graphs and Solvabilizers   The non-solvable graph of a finite group G is a simple graph whose vertices
are the elements of G and there is an edge between x and y if and only if the
subgroup generated by x and y is not solvable. The isolated vertices in the
non-solvable graph are exactly the elements of the solvable radical of G. Given
a finite group G and element x of G, the solvabilizer of x with respect to G is
the set of all elements y of G such that the subgroup generated by x and y is
solvable. The purpose of this paper is to study some properties of the
non-solvable graph and the structure of the solvabilizer of x with respect to G
for every element x of G.

19
The categories of this paper are: eess
21
The categories of this paper are: adap-org
33
The categories of this paper are: plasm-ph
3
The categories of this paper are: physics
15
The categories of this paper are: nucl-ex
9
The categories of this paper are: nlin
25
The categories of this paper are: patt-sol
24
The categories of this paper are: dg-ga
5
The categories of this paper are: gr-qc
1
The categories of this paper are: cs
8
The categories of this paper are: hep-ex
13
The categories of this paper are: quant-ph
4
The categories of this paper are: cond-mat
27
The categories of this paper are: comp-gas
22
The categories of this paper are: chao-dyn
32
The categories of this paper are: atom-ph