| | |
| | |
Stat |
Members: 3643 Articles: 2'487'895 Articles rated: 2609
29 March 2024 |
|
| | | |
|
Article overview
| |
|
Profinite groups and centralizers of coprime automorphisms whose elements are Engel | Cristina Acciarri
; Danilo Sanção da Silveira
; | Date: |
20 Jul 2017 | Abstract: | Let $q$ be a prime, $n$ a positive integer and $A$ an elementary abelian
group of order $q^r$ with $rgeq2$ 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 $ain A^#$, then $gamma_{r-1}(G)$ is $k$-Engel for some
${n,q,r}$-bounded number $k$, and if, for some integer $d$ such that $2^dleq
r-1$, all elements in the $d$th derived group of $C_G(a)$ are $n$-Engel in $G$
for any $ain A^#$, then the $d$th derived group $G^{(d)}$ is $k$-Engel for
some ${n,q,r}$-bounded number $k$.
Assuming $rgeq 3$ we prove that if all elements in $gamma_{r-2}(C_G(a))$
are $n$-Engel in $C_G(a)$ for any $ain A^#$, then $gamma_{r-2}(G)$ is
$k$-Engel for some ${n,q,r}$-bounded number $k$, and if, for some integer $d$
such that $2^dleq r-2$, all elements in the $d$th derived group of $C_G(a)$
are $n$-Engel in $C_G(a)$ for any $ain A^#,$ 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. | Source: | arXiv, 1707.6889 | Services: | Forum | Review | PDF | Favorites |
|
|
No review found.
Did you like this article?
Note: answers to reviews or questions about the article must be posted in the forum section.
Authors are not allowed to review their own article. They can use the forum section.
browser claudebot
|
| |
|
|
|
| News, job offers and information for researchers and scientists:
| |