Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Profinite groups and centralizers of coprime automorphisms whose
  elements are Engel   Let $q$ be a prime, $n$ a positive integer and $A$ an elementary abelian
group of order $q^r$ with $r\geq2$ acting on a finite $q'$-group $G$. The
following results are proved.
  We show that if all elements in $\gamma_{r-1}(C_G(a))$ are $n$-Engel in $G$
for any $a\in A^\#$, then $\gamma_{r-1}(G)$ is $k$-Engel for some
$\{n,q,r\}$-bounded number $k$, and if, for some integer $d$ such that $2^d\leq
r-1$, all elements in the $d$th derived group of $C_G(a)$ are $n$-Engel in $G$
for any $a\in A^\#$, then the $d$th derived group $G^{(d)}$ is $k$-Engel for
some $\{n,q,r\}$-bounded number $k$.
  Assuming $r\geq 3$ we prove that if all elements in $\gamma_{r-2}(C_G(a))$
are $n$-Engel in $C_G(a)$ for any $a\in A^\#$, then $\gamma_{r-2}(G)$ is
$k$-Engel for some $\{n,q,r\}$-bounded number $k$, and if, for some integer $d$
such that $2^d\leq r-2$, all elements in the $d$th derived group of $C_G(a)$
are $n$-Engel in $C_G(a)$ for any $a\in A^\#,$ then the $d$th derived group
$G^{(d)}$ is $k$-Engel for some $\{n,q,r\}$-bounded number $k$.
  Analogue (non-quantitative) results for profinite groups are also obtained.

14
The categories of this paper are: math-ph
1
The categories of this paper are: cs
16
The categories of this paper are: stat
15
The categories of this paper are: nucl-ex
0
The categories of this paper are: hep-ph
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
33
The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat
21
The categories of this paper are: adap-org
27
The categories of this paper are: comp-gas
30
The categories of this paper are: q-alg
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The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom
20
The categories of this paper are: acc-phys
34
The categories of this paper are: chem-ph