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

B. A. F. Wehrfritz

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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
Received: 27 August 2015
First available in Project Euclid: 22 December 2016

Permanent link to this document
https://projecteuclid.org/euclid.pm/1482375633

Digital Object Identifier
doi:10.5565/PUBLMAT_61117_11

Mathematical Reviews number (MathSciNet)
MR3590123

Zentralblatt MATH identifier
06697034

Subjects
Primary: 20F45: Engel conditions 20F19: Generalizations of solvable and nilpotent groups 20H25: Other matrix groups over rings

Keywords
Engel elements linear groups stability groups

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


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