Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: From Thompson to Baer-Suzuki: a sharp characterization of the solvable
  radical   We prove that an element $g$ of prime order $>3$ belongs to the solvable
radical $R(G)$ of a finite (or, more generally, a linear) group if and only if
for every $x\in G$ the subgroup generated by $g, xgx^{-1}$ is solvable. This
theorem implies that a finite (or a linear) group $G$ is solvable if and only
if in each conjugacy class of $G$ every two elements generate a solvable
subgroup.

32
The categories of this paper are: atom-ph
17
The categories of this paper are: q-fin
20
The categories of this paper are: acc-phys
7
The categories of this paper are: hep-th
21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin
10
The categories of this paper are: q-bio
36
The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom
34
The categories of this paper are: chem-ph
12
The categories of this paper are: nucl-th
22
The categories of this paper are: chao-dyn
24
The categories of this paper are: dg-ga
19
The categories of this paper are: eess
13
The categories of this paper are: quant-ph
35
The categories of this paper are: mtrl-th