## Publicacions Matemàtiques

### Right Engel elements of stability groups of general series in vector spaces

B. A. F. Wehrfritz

#### Abstract

Let $V$ be an arbitrary vector space over some division ring $D$, $\mathbf{L}$ a general series of subspaces of $V$ covering all of $V\backslash \{0\}$ and $S$ the full stability subgroup of $\mathbf{L}$ in $\operatorname{GL}(V)$. We prove that always the set of bounded right Engel elements of $S$ is equal to the $\omega$-th term of the upper central series of $S$ and that the set of right Engel elements of $S$ is frequently equal to the hypercentre of $S$.

#### Article information

Source
Publ. Mat., Volume 61, Number 1 (2017), 283-289.

Dates
First available in Project Euclid: 22 December 2016

https://projecteuclid.org/euclid.pm/1482375633

Digital Object Identifier
doi:10.5565/PUBLMAT_61117_11

Mathematical Reviews number (MathSciNet)
MR3590123

Zentralblatt MATH identifier
06697034

#### Citation

Wehrfritz, B. A. F. Right Engel elements of stability groups of general series in vector spaces. Publ. Mat. 61 (2017), no. 1, 283--289. doi:10.5565/PUBLMAT_61117_11. https://projecteuclid.org/euclid.pm/1482375633