Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The nilpotency of finite groups with a fix-point-free automorphism
  satisfying an identity   We generalize the positive solution of the Frobenius conjecture and
refinements thereof by studying the structure of groups that admit a
fix-point-free automorphism satisfying an identity.
  We show, in particular, that for every polynomial $r(t) = a_0 + a_1 \cdot t +
\cdots + a_d \cdot t^d \in \mathbb{Z}[t]$ that is irreducible over
$\mathbb{Q}$, there exist (explicit) invariants $a,b,c \in \mathbb{N}$ with the
following property. Consider a finite group with a fix-point-free automorphism
${\alpha}:{G}\longrightarrow{G}$ and suppose that for all $x \in G$ we have the
equality $x^{a_0} \cdot \alpha(x^{a_1}) \cdot \alpha^2(x^{a_2})\cdots
\alpha^d(x^{a_d}) = 1_G.$ Then $G$ is solvable and of the form $A \cdot (B
\rtimes (C \times D))$, where $A$ is an $a$-group, $B$ is a $b$-group, $C$ is a
nilpotent $c$-group, and $D$ is a nilpotent group of class at most $d^{2^d}$.
Here, a group $H$ is said to be an $a$-group (resp. $b$-group or $c$-group) if
the order of every $h \in H$ divides some natural power of $a$ (resp. $b$ or
$c$).

31
The categories of this paper are: ao-sci
0
The categories of this paper are: hep-ph
30
The categories of this paper are: q-alg
19
The categories of this paper are: eess
4
The categories of this paper are: cond-mat
9
The categories of this paper are: nlin
14
The categories of this paper are: math-ph
22
The categories of this paper are: chao-dyn
26
The categories of this paper are: bayes-an
8
The categories of this paper are: hep-ex
10
The categories of this paper are: q-bio
21
The categories of this paper are: adap-org
7
The categories of this paper are: hep-th
11
The categories of this paper are: hep-lat
12
The categories of this paper are: nucl-th
17
The categories of this paper are: q-fin