Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Finite Groups with 6 or 7 Automorphism Orbits   Let $G$ be a group. The orbits of the natural action of $\mbox{Aut}(G)$ on
$G$ are called "automorphism orbits" of $G$, and the number of automorphism
orbits of $G$ is denoted by $\omega(G)$. In this paper the finite nonsolvable
groups $G$ with $\omega(G) \leq 6$ are classified - this solves a problem posed
by Markus Stroppel - and it is proved that there are infinitely many finite
nonsolvable groups $G$ with $\omega(G)=7$. Moreover it is proved that for a
given number $n$ there are only finitely many finite groups $G$ without
nontrivial abelian normal subgroups and such that $\omega(G) \leq n$,
generalizing a result of Kohl.

28
The categories of this paper are: alg-geom
1
The categories of this paper are: cs
17
The categories of this paper are: q-fin
25
The categories of this paper are: patt-sol
14
The categories of this paper are: math-ph
29
The categories of this paper are: funct-an
9
The categories of this paper are: nlin
3
The categories of this paper are: physics
5
The categories of this paper are: gr-qc
32
The categories of this paper are: atom-ph
10
The categories of this paper are: q-bio
22
The categories of this paper are: chao-dyn
33
The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat
20
The categories of this paper are: acc-phys
31
The categories of this paper are: ao-sci